ca_ising_magnetisation_example.cc File Reference

Phase 8 example: Ising spins with Glauber dynamics + temperature sweep. More...

#include <algorithm>
#include <array>
#include <cmath>
#include <cstddef>
#include <cstdint>
#include <iomanip>
#include <iostream>
#include <random>
#include <string>
#include <ca-rng.H>
#include <ca-traits.H>
#include <tpl_ca_engine.H>
#include <tpl_ca_lattice.H>
#include <tpl_ca_neighborhood.H>
#include <tpl_ca_storage.H>
#include <tpl_ca_stochastic_rules.H>

Include dependency graph for ca_ising_magnetisation_example.cc:

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Functions
int	main ()

Detailed Description

Phase 8 example: Ising spins with Glauber dynamics + temperature sweep.

Builds a 32x32 toroidal Ising lattice with Von-Neumann neighbours (degree 4) and runs the Glauber single-spin-flip dynamics from a disordered initial state. The example sweeps a small grid of temperatures (T = 1.0, 2.0, 2.27, 2.5, 4.0) and reports, for each temperature, the average absolute magnetisation per site after a burn-in.

The exact 2-D Ising critical temperature on the square lattice is T_c = 2 * J / ln(1 + sqrt(2)) ~ 2.269 J so we expect:

• T < T_c: ordered phase, |m| close to 1.
• T ~ T_c: critical fluctuations.
• T > T_c: disordered phase, |m| close to 0.

After the sweep we render the final spin configuration of the cold, critical, and hot regimes so the visual contrast is obvious.

Glyphs: '+' spin up '-' spin down

Definition in file ca_ising_magnetisation_example.cc.

Function Documentation

main()

int main

(

void

)

Definition at line 139 of file ca_ising_magnetisation_example.cc.

References bar(), Aleph::blossom_maximum_cardinality_matching(), cols, k, r, rows, and seed.