This project implements Monte Carlo simulations for studying thermal phase transitions using PyTorch. It leverages CUDA acceleration, a checkerboard (alternating) Metropolis update scheme, and parallel tempering to improve sampling efficiency. Models implemented include the XY model, Ising model, and q-state Potts model.
Ising model Demo
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CUDA Acceleration:
Utilize GPU computing to significantly speed up the simulation process. -
Checkerboard Metropolis Update:
The simulation adopts a checkerboard update pattern. This allows for efficient and parallel updates of the lattice by splitting it into two interleaved sub-lattices. -
Parallel Tempering:
Enhance sampling efficiency by exchanging configurations between different temperature chains. This is particularly useful near critical points and low temperature region to overcome local minima and achieve better convergence. -
Automatic Mixed Precision (AMP):
Enable automatic mixed precision to leverage Tensor Cores on compatible GPUs for faster computation.
Monte Carlo simulations in statistical physics help explore phase transitions and critical phenomena. The simulation uses the Metropolis algorithm with the acceptance probability
$$
P_{\text{acc}} = \min\left(1, \exp\left(-\frac{\Delta E}{T}\right)\right)
$$
where
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XY Model:
Spins are continuous, represented by an angle$\left(\theta \in [0, 2\pi)\right)$ .
Energy:
$$ E = -J \sum_{\langle i,j \rangle} \cos(\theta_i - \theta_j) $$ Adaptive updates can be applied to adjust the angular perturbation dynamically. -
Ising Model:
Spins take values$\left(\pm1\right)$ .
Energy:
$$ E = -J \sum_{\langle i,j \rangle} s_i s_j $$ -
Potts Model:
Spins take integer values in$\left({0, 1, \dots, q-1}\right)$ .
Energy is computed using the Kronecker delta: $$ E = -J \sum_{\langle i,j \rangle} \delta(s_i, s_j) $$
- Python 3.9 or higher
- PyTorch with CUDA support (if using GPU acceleration)
- Other dependencies as listed in the provided
requirements.txt