Druyd:Knowledge

Modelo de Ising

Storyboard

Ising's model creates an iterative algorithm to solve the problem of permanent magnetization. A simplified version is shown in this chapter. The real one, which was Ising's thesis, shows that a one-dimensional chain cannot maintain a magnetic field without permanent magnetization. However, it is also the problem for a two-dimensional system and shows that in that case there is permanent magnetization.

>Model

ID:(540, 0)

Modelo de Ising

Model

Variables

Symbol

Text

Variable

Value

Units

Calculate

MKS Value

MKS Units

$H$

Campo magnético

kg/C s

$H_i$

H_i

Campo magnético de Ising

kg/C s

$H_{eff}$

H_eff

Campo magnético efectivo

kg/C s

$H_0$

H_0

Campo magnético externo

kg/C s

$\bar{H}$

Campo magnético medio

kg/C s

$J$

Constante de acoplamiento

kg m^2

$k_B$

k_B

Constante de Boltzmann

kg m^2/s^2 K

$E$

Energía total

$\beta$

beta

Factor $\beta$

C m^2/s

$N$

Números de partículas

$n$

Números de vecinos con que existe interacción

$\gamma$

gamma

Radio giroscópico

C/kg

$S_j$

S_j

Spin de la partícula $j$

kg m^2/s

$S_k$

S_k

Spin de la partícula $k$

kg m^2/s

$\bar{S}$

Spin medio

kg m^2/s

$\bar{S}_i$

mS_i

Spin medio, iteración $k$

kg m^2/s

$\bar{S}_{i+1}$

mS_i1

Spin medio, iteración $k+1$

kg m^2/s

$T$

Temperatura

$T_i$

T_i

Temperatura de Ising

Calculations

Equation

Number

First, select the equation:

, then, select the variable:

Symbol

Equation

Solved

Translated

Calculations

Symbol

Equation

Solved

Translated

Variable

Given

Calculate

Target :

Equation

To be used

Equations

$ E =- g\gamma H \displaystyle\sum_{ j = 1}^ N S_j -2 J \displaystyle\sum_{ j =1}^ N \displaystyle\sum_{ k = 1}^ n S_j S_k $

E =- g * gamma * H @SUM( S_j , j , 1 , N )-2* J @SUM( S_j * @SUM( S_k , k , 1 , n ) , j , 1 , N )

(ID 3915)

$ H_{eff} = H +\displaystyle\frac{ J }{2 g \gamma }\sum_{ k =1}^ n S_k $

H_eff = H + J * @SUM( S_k , k , 1 , n )/(2* g * gamma )

(ID 4836)

$ \bar{S} =\tanh( \beta g \gamma \bar{H} )$

S =tanh( beta * g * gamma * H_m )

(ID 4837)

$ H_{eff} = H +\displaystyle\frac{ J }{2 g \gamma } \bar{S} $

H_eff = H + J * S /(2* g * gamma )

(ID 4838)

$ \bar{S} =\tanh\left( \beta g \gamma H + \beta n \displaystyle\frac{ J }{2} \bar{S} \right)$

mS =tanh( beta * g * gamma * H + beta * n * J * mS /2)

(ID 4839)

$ T_i =\displaystyle\frac{ n J }{2 k_B }$

T_i = n * J /(2* k_B )

(ID 4840)

$ H_i =\displaystyle\frac{ k_B T_i }{ g \gamma }$

H_i = k_B * T_i /( g * gamma )

(ID 4841)

$ \bar{S} =\tanh\left(\displaystyle\frac{ T_i }{ T }\left(\displaystyle\frac{ H }{ H_i }+ \bar{S} \right)\right)$

mS =tanh( T_i * H /( T * H_i )+ mS )

(ID 4842)

$ \bar{S}_{k+1} =\tanh\left(\displaystyle\frac{ T_c }{ T }\left(\displaystyle\frac{ H }{ H_c }+ \bar{S}_k \right)\right)$

mS_k1 =tanh( T_c * H /( T * H_c )+ mS_k )

(ID 4843)

Examples

ID:(540, 0)