Ising rule with Glauber single-spin-flip dynamics. More...

#include <tpl_ca_stochastic_rules.H>

Public Types
using	engine_type = Engine

Public Member Functions
	Ising_Glauber_Rule (const double T, const double J=1.0, const double H=0.0, const std::uint64_t master_seed=0)
	Build a Glauber Ising rule.

double	temperature () const noexcept

double	coupling () const noexcept

double	field () const noexcept

std::uint64_t	master_seed () const noexcept

void	set_master_seed (std::uint64_t s) noexcept

template<typename State , std::size_t Rank>
State	operator() (const State &current, Neighbor_View< State > neighbours, const Cell_Context< Rank > &ctx) const
	Compute the next Ising state for cell `current`.

Private Attributes
double	T_

double	J_

double	H_

std::uint64_t	master_seed_

Detailed Description

template<typename Engine = std::mt19937_64>
class Aleph::CA::Ising_Glauber_Rule< Engine >

Ising rule with Glauber single-spin-flip dynamics.

At each cell the flip probability is

p_flip = 1 / (1 + exp(deltaE / T))

where deltaE = 2 * s * (J * sum_neighbours + H). Glauber dynamics satisfy detailed balance and converge to the canonical Boltzmann distribution for the Ising Hamiltonian

H = -J * sum_<i,j> s_i s_j - H * sum_i s_i.

Cell states must be integral. Signed types are treated as ±1; unsigned types as {0, 1} (with 0 representing spin -1).

Template Parameters

Engine RNG engine; defaults to std::mt19937_64.

Definition at line 399 of file tpl_ca_stochastic_rules.H.

Member Typedef Documentation

◆ engine_type

template<typename Engine = std::mt19937_64>

using Aleph::CA::Ising_Glauber_Rule< Engine >::engine_type = Engine

Definition at line 407 of file tpl_ca_stochastic_rules.H.

Constructor & Destructor Documentation

◆ Ising_Glauber_Rule()

template<typename Engine = std::mt19937_64>

Aleph::CA::Ising_Glauber_Rule< Engine >::Ising_Glauber_Rule	(	const double	T,
		const double	J = `1.0`,
		const double	H = `0.0`,
		const std::uint64_t	master_seed = `0`
	)

inline

Build a Glauber Ising rule.

Parameters

[in]	T	temperature; must be strictly positive.
[in]	J	coupling constant (default `+1`, ferromagnetic).
[in]	H	external magnetic field (default `0`).
[in]	master_seed	master seed forwarded to `cell_seed()`.

Exceptions

std::domain_error if T <= 0.

Definition at line 417 of file tpl_ca_stochastic_rules.H.

References ah_domain_error_if.

Member Function Documentation

◆ coupling()

template<typename Engine = std::mt19937_64>

double Aleph::CA::Ising_Glauber_Rule< Engine >::coupling ( ) const

inlinenoexcept

Definition at line 431 of file tpl_ca_stochastic_rules.H.

References Aleph::CA::Ising_Glauber_Rule< Engine >::J_.

◆ field()

template<typename Engine = std::mt19937_64>

double Aleph::CA::Ising_Glauber_Rule< Engine >::field ( ) const

inlinenoexcept

Definition at line 436 of file tpl_ca_stochastic_rules.H.

References Aleph::CA::Ising_Glauber_Rule< Engine >::H_.

◆ master_seed()

template<typename Engine = std::mt19937_64>

std::uint64_t Aleph::CA::Ising_Glauber_Rule< Engine >::master_seed ( ) const

inlinenoexcept

Definition at line 441 of file tpl_ca_stochastic_rules.H.

References Aleph::CA::Ising_Glauber_Rule< Engine >::master_seed_.

◆ operator()()

template<typename Engine = std::mt19937_64>

template<typename State , std::size_t Rank>

State Aleph::CA::Ising_Glauber_Rule< Engine >::operator()	(	const State &	current,
		Neighbor_View< State >	neighbours,
		const Cell_Context< Rank > &	ctx
	)		const