TFIMSimulation class

class TFIMSimulation(size=10, beta=0.4, h=0.05, steps=100)

A class to simulate the Transverse Field Ising Model (TFIM) on a two-dimensional lattice. The TFIM is a model of magnetism in statistical mechanics.

Parameters:

• size (int, optional) – The width and height of the square lattice. Defaults to 10.

• beta (float, optional) – The inverse temperature parameter for the simulation. Defaults to 0.4.

• h (float, optional) – The transverse field strength applied to the system. Defaults to 0.05.

• steps (int, optional) – The number of Monte Carlo steps to perform in the simulation. Defaults to 100.

size

The size of the lattice (size x size).

beta

The inverse temperature parameter for the simulation.

h

The transverse field strength.

steps

The number of simulation steps to run.

lattice

The lattice representing the spins, initialized randomly.

initialize_lattice()

Initializes the lattice to a random state where each spin is either up or down with equal probability.

Returns:

A square lattice of spins.

Return type:

torch.Tensor

tfim_step()

Performs a single Monte Carlo step in the TFIM simulation, potentially flipping each spin based on the Metropolis-Hastings algorithm.

run_simulation()

Runs the TFIM simulation for the number of steps specified in the constructor.

plot_lattice()

Plots the current state of the lattice using matplotlib, showing the spins as a heatmap.

Example Usage

The following example sets up a TFIM simulation with a lattice of size 10x10, runs it for 100 steps, and then plots the final configuration of spins:

# Initialize the TFIM simulation
sim = TFIMSimulation(size=10, beta=0.4, h=0.05, steps=100)

# Run the simulation
sim.run_simulation()

# Plot the final lattice configuration
sim.plot_lattice()

This will produce a plot showing the spin configuration of the lattice after running the specified number of Monte Carlo steps.