build based on 920c134

previews/PR208/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2024-01-10T15:16:15","documenter_version":"1.2.1"}}
+{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2024-01-11T21:03:23","documenter_version":"1.2.1"}}

previews/PR208/assets/notebooks/03_LLD_CoRh2O4.ipynb

@@ -81,43 +81,28 @@
    "cell_type": "code",
    "source": [
     "λ  = 0.2             # Magnitude of damping (dimensionless)\n",
-    "kT = 16 * meV_per_K  # 16K, a temperature slightly below ordering"
+    "kT = 16 * meV_per_K  # 16K, a temperature slightly below ordering\n",
+    "langevin = Langevin(; λ, kT)"
    ],
    "metadata": {},
    "execution_count": null
   },
   {
    "cell_type": "markdown",
    "source": [
-    "Use `suggest_timestep` to obtain a reasonable integration timestep.\n",
-    "The spin configuration in `sys` should ideally be equilibrated for the target\n",
-    "temperature `kT`, but the current, energy-minimized configuration will also\n",
-    "work reasonably well. Usually `tol=1e-2` is good tolerance to numerical error."
+    "Use `suggest_timestep` to select an integration timestep for the given\n",
+    "error tolerance, e.g. `tol=1e-2`. The spin configuration in `sys` should\n",
+    "ideally be relaxed into thermal equilibrium, but the current, energy-minimized\n",
+    "configuration will also work reasonably well."
    ],
    "metadata": {}
   },
   {
    "outputs": [],
    "cell_type": "code",
    "source": [
-    "suggest_timestep(sys; tol=1e-2, λ, kT)"
-   ],
-   "metadata": {},
-   "execution_count": null
-  },
-  {
-   "cell_type": "markdown",
-   "source": [
-    "We now have all data needed to construct a Langevin integrator."
-   ],
-   "metadata": {}
-  },
-  {
-   "outputs": [],
-   "cell_type": "code",
-   "source": [
-    "Δt = 0.025\n",
-    "langevin = Langevin(Δt; λ, kT);"
+    "suggest_timestep(sys, langevin; tol=1e-2)\n",
+    "langevin.Δt = 0.025"
    ],
    "metadata": {},
    "execution_count": null
@@ -146,16 +131,17 @@
   {
    "cell_type": "markdown",
    "source": [
-    "Calling `check_timestep` indicates that our choice of `Δt` was a\n",
-    "little smaller than necessary; increasing it will improve efficiency."
+    "Now that the spin configuration has relaxed, we can learn that `Δt` was a\n",
+    "little smaller than necessary; increasing it will make the remaining\n",
+    "simulations faster."
    ],
    "metadata": {}
   },
   {
    "outputs": [],
    "cell_type": "code",
    "source": [
-    "check_timestep(sys, langevin; tol=1e-2)\n",
+    "suggest_timestep(sys, langevin; tol=1e-2)\n",
     "langevin.Δt = 0.042"
    ],
    "metadata": {},

previews/PR208/assets/notebooks/04_GSD_FeI2.ipynb

@@ -106,8 +106,8 @@
   {
    "cell_type": "markdown",
    "source": [
-    "As previously observed, direct energy minimization is susceptible to trapping\n",
-    "in a local energy minimum."
+    "As previously observed\"), direct energy minimization is susceptible to trapping in a local\n",
+    "energy minimum."
    ],
    "metadata": {}
   },
@@ -138,53 +138,39 @@
    "cell_type": "code",
    "source": [
     "λ  = 0.2  # Dimensionless damping time-scale\n",
-    "kT = 0.2  # Temperature in meV"
+    "kT = 0.2  # Temperature in meV\n",
+    "langevin = Langevin(; λ, kT)"
    ],
    "metadata": {},
    "execution_count": null
   },
   {
    "cell_type": "markdown",
    "source": [
-    "Use `suggest_timestep` to obtain a reasonable integration timestep. It\n",
-    "is important that the system has already been initialized to a low-energy\n",
-    "configuration. Usually `tol=1e-2` is good tolerance to numerical error."
+    "Use `suggest_timestep` to select an integration timestep for the given\n",
+    "error tolerance, e.g. `tol=1e-2`. The spin configuration in `sys` should\n",
+    "ideally be relaxed into thermal equilibrium, but the current, energy-minimized\n",
+    "configuration will also work reasonably well."
    ],
    "metadata": {}
   },
   {
    "outputs": [],
    "cell_type": "code",
    "source": [
-    "suggest_timestep(sys; tol=1e-2, λ, kT)"
+    "suggest_timestep(sys, langevin; tol=1e-2)\n",
+    "langevin.Δt = 0.027"
    ],
    "metadata": {},
    "execution_count": null
   },
   {
    "cell_type": "markdown",
    "source": [
-    "This information is sufficient to define the Langevin integrator."
-   ],
-   "metadata": {}
-  },
-  {
-   "outputs": [],
-   "cell_type": "code",
-   "source": [
-    "Δt = 0.027\n",
-    "langevin = Langevin(Δt; kT, λ);"
-   ],
-   "metadata": {},
-   "execution_count": null
-  },
-  {
-   "cell_type": "markdown",
-   "source": [
-    "Langevin dynamics can be used to search for a magnetically ordered state. This\n",
-    "works well because the temperature `kT = 0.2` has been carefully selected. It\n",
-    "is below the ordering temperature, but large enough that the dynamical\n",
-    "trajectory can overcome local energy barriers and annihilate defects."
+    "Sample spin configurations using Langevin dynamics. We have carefully selected\n",
+    "a temperature of 0.2 eV that is below the ordering temperature, but large\n",
+    "enough to that the dynamics can overcome local energy barriers and annihilate\n",
+    "defects."
    ],
    "metadata": {}
   },
@@ -202,7 +188,7 @@
   {
    "cell_type": "markdown",
    "source": [
-    "Calling `check_timestep` shows that thermalization has not\n",
+    "Calling `suggest_timestep` shows that thermalization has not\n",
     "substantially altered the suggested `Δt`."
    ],
    "metadata": {}
@@ -211,7 +197,7 @@
    "outputs": [],
    "cell_type": "code",
    "source": [
-    "check_timestep(sys, langevin; tol=1e-2)"
+    "suggest_timestep(sys, langevin; tol=1e-2)"
    ],
    "metadata": {},
    "execution_count": null
@@ -297,7 +283,7 @@
    "outputs": [],
    "cell_type": "code",
    "source": [
-    "check_timestep(sys_large, langevin; tol=1e-2)\n",
+    "suggest_timestep(sys_large, langevin; tol=1e-2)\n",
     "langevin.Δt = 0.040"
    ],
    "metadata": {},

previews/PR208/assets/scripts/03_LLD_CoRh2O4.jl

@@ -16,19 +16,18 @@ sys = resize_supercell(sys, (10, 10, 10))
 
 λ  = 0.2             # Magnitude of damping (dimensionless)
 kT = 16 * meV_per_K  # 16K, a temperature slightly below ordering
+langevin = Langevin(; λ, kT)
 
-suggest_timestep(sys; tol=1e-2, λ, kT)
-
-Δt = 0.025
-langevin = Langevin(Δt; λ, kT);
+suggest_timestep(sys, langevin; tol=1e-2)
+langevin.Δt = 0.025
 
 energies = [energy_per_site(sys)]
 for _ in 1:1000
     step!(sys, langevin)
     push!(energies, energy_per_site(sys))
 end
 
-check_timestep(sys, langevin; tol=1e-2)
+suggest_timestep(sys, langevin; tol=1e-2)
 langevin.Δt = 0.042
 
 plot(energies, color=:blue, figure=(size=(600,300),), axis=(xlabel="Timesteps", ylabel="Energy (meV)"))

previews/PR208/assets/scripts/04_GSD_FeI2.jl

@@ -41,17 +41,16 @@ plot_spins(sys; color=[s[3] for s in sys.dipoles])
 
 λ  = 0.2  # Dimensionless damping time-scale
 kT = 0.2  # Temperature in meV
+langevin = Langevin(; λ, kT)
 
-suggest_timestep(sys; tol=1e-2, λ, kT)
-
-Δt = 0.027
-langevin = Langevin(Δt; kT, λ);
+suggest_timestep(sys, langevin; tol=1e-2)
+langevin.Δt = 0.027
 
 for _ in 1:10_000
     step!(sys, langevin)
 end
 
-check_timestep(sys, langevin; tol=1e-2)
+suggest_timestep(sys, langevin; tol=1e-2)
 
 plot_spins(sys; color=[s[3] for s in sys.dipoles])
 
@@ -64,7 +63,7 @@ for _ in 1:10_000
     step!(sys_large, langevin)
 end
 
-check_timestep(sys_large, langevin; tol=1e-2)
+suggest_timestep(sys_large, langevin; tol=1e-2)
 langevin.Δt = 0.040
 
 Δt = 2*langevin.Δt

previews/PR208/examples/01_LSWT_SU3_FeI2.html

@@ -156,4 +156,4 @@
 fig = Figure()
 ax = Axis(fig[1,1]; xlabel="Momentum (r.l.u.)", ylabel="Energy (meV)", xticks, xticklabelrotation=π/6)
 heatmap!(ax, 1:size(is_averaged, 1), energies, is_averaged)
-fig</code></pre><img src="01_LSWT_SU3_FeI2-5ad5f204.png" alt="Example block output"/><p>This result can be directly compared to experimental neutron scattering data from <a href="https://doi.org/10.1038/s41567-020-01110-1">Bai et al.</a></p><img src="https://raw.githubusercontent.com/SunnySuite/Sunny.jl/main/docs/src/assets/FeI2_intensity.jpg"><p>(The publication figure accidentally used a non-standard coordinate system to label the wave vectors.)</p><p>To get this agreement, the use of SU(3) coherent states is essential. In other words, we needed a theory of multi-flavored bosons. The lower band has large quadrupolar character, and arises from the strong easy-axis anisotropy of FeI₂. By setting <code>mode = :SUN</code>, the calculation captures this coupled dipole-quadrupole dynamics.</p><p>An interesting exercise is to repeat the same study, but using <code>mode = :dipole</code> instead of <code>:SUN</code>. That alternative choice would constrain the coherent state dynamics to the space of dipoles only.</p><p>The full dynamical spin structure factor (DSSF) can be retrieved as a <span>$3×3$</span> matrix with the <a href="../library.html#Sunny.dssf-Tuple{SpinWaveTheory, Any}"><code>dssf</code></a> function, for a given path of <span>$𝐪$</span>-vectors.</p><pre><code class="language-julia hljs">disp, is = dssf(swt, path);</code></pre><p>The first output <code>disp</code> is identical to that obtained from <code>dispersion</code>. The second output <code>is</code> contains a list of <span>$3×3$</span> matrix of intensities. For example, <code>is[q,n][2,3]</code> yields the <span>$(ŷ,ẑ)$</span> component of the structure factor intensity for <code>nth</code> mode at the <code>q</code>th wavevector in the <code>path</code>.</p><h2 id="What&#39;s-next?"><a class="docs-heading-anchor" href="#What&#39;s-next?">What&#39;s next?</a><a id="What&#39;s-next?-1"></a><a class="docs-heading-anchor-permalink" href="#What&#39;s-next?" title="Permalink"></a></h2><p>The multi-boson linear spin wave theory, applied above, can be understood as the quantization of a certain generalization of the Landau-Lifshitz spin dynamics. Rather than dipoles, this dynamics takes places on the space of <a href="https://arxiv.org/abs/2106.14125">SU(<em>N</em>) coherent states</a>.</p><p>The full SU(<em>N</em>) coherent state dynamics, with appropriate quantum correction factors, can be useful to model finite temperature scattering data. In particular, it captures certain anharmonic effects due to thermal fluctuations. See our <a href="04_GSD_FeI2.html#4.-Generalized-spin-dynamics-of-FeI-at-finite-*T*">generalized spin dynamics tutorial</a>.</p><p>The classical dynamics is also a good starting point to study non-equilibrium phenomena. Empirical noise and damping terms can be used to model <a href="https://arxiv.org/abs/2209.01265">coupling to a thermal bath</a>. This yields a Langevin dynamics of SU(<em>N</em>) coherent states. Our <a href="06_CP2_Skyrmions.html#6.-Dynamical-quench-into-CP-skyrmion-liquid">dynamical SU(<em>N</em>) quench</a> tutorial illustrates how a temperature quench can give rise to novel liquid phase of CP² skyrmions.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../index.html">« Overview</a><a class="docs-footer-nextpage" href="02_LSWT_CoRh2O4.html">2. Spin wave simulations of CoRh₂O₄ »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Wednesday 10 January 2024 15:16">Wednesday 10 January 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+fig</code></pre><img src="01_LSWT_SU3_FeI2-5ad5f204.png" alt="Example block output"/><p>This result can be directly compared to experimental neutron scattering data from <a href="https://doi.org/10.1038/s41567-020-01110-1">Bai et al.</a></p><img src="https://raw.githubusercontent.com/SunnySuite/Sunny.jl/main/docs/src/assets/FeI2_intensity.jpg"><p>(The publication figure accidentally used a non-standard coordinate system to label the wave vectors.)</p><p>To get this agreement, the use of SU(3) coherent states is essential. In other words, we needed a theory of multi-flavored bosons. The lower band has large quadrupolar character, and arises from the strong easy-axis anisotropy of FeI₂. By setting <code>mode = :SUN</code>, the calculation captures this coupled dipole-quadrupole dynamics.</p><p>An interesting exercise is to repeat the same study, but using <code>mode = :dipole</code> instead of <code>:SUN</code>. That alternative choice would constrain the coherent state dynamics to the space of dipoles only.</p><p>The full dynamical spin structure factor (DSSF) can be retrieved as a <span>$3×3$</span> matrix with the <a href="../library.html#Sunny.dssf-Tuple{SpinWaveTheory, Any}"><code>dssf</code></a> function, for a given path of <span>$𝐪$</span>-vectors.</p><pre><code class="language-julia hljs">disp, is = dssf(swt, path);</code></pre><p>The first output <code>disp</code> is identical to that obtained from <code>dispersion</code>. The second output <code>is</code> contains a list of <span>$3×3$</span> matrix of intensities. For example, <code>is[q,n][2,3]</code> yields the <span>$(ŷ,ẑ)$</span> component of the structure factor intensity for <code>nth</code> mode at the <code>q</code>th wavevector in the <code>path</code>.</p><h2 id="What&#39;s-next?"><a class="docs-heading-anchor" href="#What&#39;s-next?">What&#39;s next?</a><a id="What&#39;s-next?-1"></a><a class="docs-heading-anchor-permalink" href="#What&#39;s-next?" title="Permalink"></a></h2><p>The multi-boson linear spin wave theory, applied above, can be understood as the quantization of a certain generalization of the Landau-Lifshitz spin dynamics. Rather than dipoles, this dynamics takes places on the space of <a href="https://arxiv.org/abs/2106.14125">SU(<em>N</em>) coherent states</a>.</p><p>The full SU(<em>N</em>) coherent state dynamics, with appropriate quantum correction factors, can be useful to model finite temperature scattering data. In particular, it captures certain anharmonic effects due to thermal fluctuations. See our <a href="04_GSD_FeI2.html#4.-Generalized-spin-dynamics-of-FeI-at-finite-*T*">generalized spin dynamics tutorial</a>.</p><p>The classical dynamics is also a good starting point to study non-equilibrium phenomena. Empirical noise and damping terms can be used to model <a href="https://arxiv.org/abs/2209.01265">coupling to a thermal bath</a>. This yields a Langevin dynamics of SU(<em>N</em>) coherent states. Our <a href="06_CP2_Skyrmions.html#6.-Dynamical-quench-into-CP-skyrmion-liquid">dynamical SU(<em>N</em>) quench</a> tutorial illustrates how a temperature quench can give rise to novel liquid phase of CP² skyrmions.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../index.html">« Overview</a><a class="docs-footer-nextpage" href="02_LSWT_CoRh2O4.html">2. Spin wave simulations of CoRh₂O₄ »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Thursday 11 January 2024 21:03">Thursday 11 January 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

previews/PR208/examples/02_LSWT_CoRh2O4.html

@@ -60,4 +60,4 @@
 fig = Figure()
 ax = Axis(fig[1,1]; xlabel="Q (Å⁻¹)", ylabel="ω (meV)")
 heatmap!(ax, radii, energies, output, colormap=:gnuplot2)
-fig</code></pre><img src="02_LSWT_CoRh2O4-19eaaa6f.png" alt="Example block output"/><p>This result can be compared to experimental neutron scattering data from Fig. 5 of <a href="https://doi.org/10.1103/PhysRevB.96.064413">Ge et al.</a></p><img width="95%" src="https://raw.githubusercontent.com/SunnySuite/Sunny.jl/main/docs/src/assets/CoRh2O4_intensity.jpg"></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="01_LSWT_SU3_FeI2.html">« 1. Multi-flavor spin wave simulations of FeI₂ (Showcase)</a><a class="docs-footer-nextpage" href="03_LLD_CoRh2O4.html">3. Landau-Lifshitz dynamics of CoRh₂O₄ at finite <em>T</em> »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Wednesday 10 January 2024 15:16">Wednesday 10 January 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+fig</code></pre><img src="02_LSWT_CoRh2O4-19eaaa6f.png" alt="Example block output"/><p>This result can be compared to experimental neutron scattering data from Fig. 5 of <a href="https://doi.org/10.1103/PhysRevB.96.064413">Ge et al.</a></p><img width="95%" src="https://raw.githubusercontent.com/SunnySuite/Sunny.jl/main/docs/src/assets/CoRh2O4_intensity.jpg"></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="01_LSWT_SU3_FeI2.html">« 1. Multi-flavor spin wave simulations of FeI₂ (Showcase)</a><a class="docs-footer-nextpage" href="03_LLD_CoRh2O4.html">3. Landau-Lifshitz dynamics of CoRh₂O₄ at finite <em>T</em> »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Thursday 11 January 2024 21:03">Thursday 11 January 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>