Questions tagged [ising-model]

The Ising model of ferromagnetism in statistical mechanics consists of discrete bimodal (+1 or −1) "spin" (moment) variables in a simple Hamiltonian interacting with their next neighbors on a lattice. The one-dimensional variant does not evince a phase transition, but the two-dimensional square-lattice one does. Use for analog and generalized discrete models on several lattices and dimensions.

Filter by
Sorted by
Tagged with
1
vote
1answer
44 views

Why does the Ising model at the critical point have scale invariance?

If my current understanding of phase transitions and the renormalization group (RG) method is true, RG is a kind of 'zooming out' process, since this procedure makes a block of neighboring spins and ...
0
votes
0answers
38 views

Critical exponent $\nu$ of 3d Ising model

this question comes from an exercise of Sethna's book "Statistical Mechanics: Entropy, Order Parameters and Complexity". it is in page 282 question 12.2 In 3d Ising model, the spin ...
1
vote
0answers
34 views

Mean Field Phase Transition of Spin Systems on a irregular graph

In the Ising model w/o external field, if we use mean-field approximation, and have the regular graph lattice... then we can use the symmetry argument to recover the fact that $$\bar{x} = \tanh{(\beta ...
0
votes
1answer
31 views

Legendre transforms for the Ising model

I'm reading a review on the Ising model and came across a section where they discuss Legendre transforms of thermodynamic potentials. Now I'm familiar with the classical thermodynamic relations such ...
1
vote
1answer
49 views

2D Ising model and FK-percolation

Consider the 2D Ising model on the finite lattice $\Lambda$ with $+$ boundary conditions, i.e., all spins outside of $\Lambda$ are $=+1$. Let $\mathscr{E}_\Lambda^b$ denote the edges in $\Lambda$ and ...
0
votes
0answers
33 views

Physical explanation of the non-analyticities in the ising model in the vicinity of zero external field

In the Ising model when $T<T_C$ with $T_C$ being the Curie temperature, there is a finite jump of the mean magnetization per spin, $m$, as the external field crosses $0$ (goes from negative values ...
1
vote
1answer
49 views

Generating Ising model steady state configurations

What is the most efficient way to simulate steady state configurations of the Ising model? I am just interested in having a large set of random steady state configurations of the 1D Ising model (with ...
2
votes
0answers
45 views

Plotting the magnetic susceptibility of the mean field Ising model

I am struggling to understand how they have ploted some functions regarding the Ising model in the mean field approximation (Curie-Weiss model) in my lecture notes For more details,you can see them ...
0
votes
1answer
34 views

Confusion about units of physical magnitudes in the Hamiltonian of the Ising model

I am having trouble with the units used in the Hamiltonian of the Ising model. I have search several notes, I have three examples in the picture below No one states explicitly what the units of the ...
2
votes
2answers
82 views

From where does the Ising Hamiltonian come?

So in my Stat Mech course, we were introduced to the classical Ising Model: $$H = -J\Sigma _{<ij>}S_iS_j - K\Sigma_i S_i$$ But from where does this come from? Is there any rationale behind this? ...
0
votes
0answers
13 views

What happens to the energy when a system following Ising Model goes to its ground state?

I'm a computer scientist and new to Ising Model. I've learned that if such a system is left to itself it will converge to its minimum energy state. Here are the questions I have: As the system is ...
0
votes
0answers
14 views

Wolff algorithm for anisotropic Ising model

Question Is there way to simulate a 2D Ising model with anisotropic coupling parameter $J_{ij}$ and zero external field using Wolff algorithm? Particularly, I am looking for when coupling parameter $...
1
vote
0answers
29 views

Simulation of Quantum Ising Model

I curious to know if there is a way to do simulation of quantum ising model with transverse field. The method I know is - do classical ising model simulation in d+1 dimension which essentially maps to ...
2
votes
0answers
26 views

Gaussianity of lattice models in statistical mechanics

Recently there was a result on triviality (or Gaussianity) of the Ising model and $\phi^4$-theory in dimension $d=4$. This therefore holds in any dimension $d \geq 4$. We also know that the 2D Ising ...
2
votes
1answer
59 views

2D Ising model exact expression for two-point function

The Ising model on $\mathbb{Z}^2$ is given by the Hamiltonian $$ H(\sigma)=-\sum_{\{x,y\}}\sigma_x\sigma_y $$ and the Gibbs measure as $$ \frac{\exp(-\beta H(\sigma))}{Z_\beta}\,. $$ There exists an ...
0
votes
1answer
60 views

Why is this the Helmholtz Free Energy for the Onsager Ising Model?

I'm reading through Kerson Huang's presentation of the Onsager solution. We end up determining that the natural log of the partition function is $$\ln Z = \frac{1}{2}\ln (\frac{2 \cosh^2(2 \beta \...
2
votes
1answer
61 views

Phase transition in parameter (and not temperature) for a classical system

Consider the $q$-state Potts model on $\mathbb{Z}^d$ for some integer $q$ - this also has an FK-representation for any real number $q$. For $d = 2$ the model is exactly solvable and has a critical ...
1
vote
1answer
54 views

Estimating the heat capacity of ising model

I am have written a Metropolis-Hastings algorithm and am currently trying to compare it to the analytical results for the 2D Ising model. The free energy seems reasonable but the heat capacity I'm ...
1
vote
0answers
19 views

Eigenvector problem for a block toeplitz matrix [closed]

Consider a 2*2 block toeplitz real matrix A . The (i,j) block is given by $$ \begin{matrix} -f_{i-j} & g_{i-j} \\ -g_{j-i} & f_{i-j} \end{matrix} $$ where i,j go from 1 to L. f satisfies $f_{-...
1
vote
0answers
45 views

Energy in the Ising model for liquid-gas transition

I am teaching myself statistical mechanics using the lecture notes of Professor Leonard Susskind. I am confused about a statement 'reducing $h$ reduces the density' at page $555$. I know the statement ...
3
votes
1answer
139 views

2D Ising model on curved surface

What will be the sensible extension of the 2D Ising to some curved surface - for instance, for a sphere or even something non-orientable? For the flat space energy is given by well-known expression: $$...
0
votes
0answers
39 views

Ising model critical temperature from divergence of the high temperature series

Consider the Ising model on a d-dimensional hypercubic lattice with nearest-neighbor coupling $J=1$: $$H=-\sum_{\langle ij \rangle}\sigma_i\sigma_j$$ For small $\beta$ (corresponding to high ...
0
votes
1answer
40 views

2D Ising model entropy as a function of external field

I am trying to figure out what is the entropy expression as a function of the external field in a 2D Ising model with nearest neighbour interaction. My Hamiltonian is the following: $\mathcal{H}=-\...
0
votes
1answer
92 views

Sum of all two point correlation functions in the Ising model

The two point correlation function for the Ising model is defined as $\left[\langle\sigma_i\sigma_j\rangle -\langle\sigma_i\rangle\langle\sigma_j\rangle\right]$. Then the sum over $i$ $j$ of that ...
0
votes
0answers
24 views

Obtain Mean Field Equations for Spin Models using a uniform Ansatz

I would like to see how my model I am working on behaves in the limit of infinite dimensions so I get a little bit of intuition for the low dimensional case. In the paper I am reading they have a ...
1
vote
1answer
94 views

What is value of critical temperature?

What is the value of critical temperature in the 2D classical ising model? My Understanding Suppose one can write the partition function for the 2D classical ising model in high-temperature expansion ...
0
votes
0answers
31 views

Transverse field Ising in 2 dimensional lattice - kronecker product

Assume we have a transverse field Ising chain (1D): $\hat H =-J\sum_{i=1}^{N}\sigma^z_i\sigma^z_{i+1}-h\sum_{i=1}^{N}\sigma^x_i$, where $\sigma^{\alpha}_i$ are the local spin operators at site i ...
0
votes
1answer
48 views

2D ising model explains phase transition (Para-ferro) in 3D space How?

2D ising model explains phase transition (Para-ferro). How come a 2-D model explain a system where spins are distributed in all three directions?
4
votes
1answer
220 views

Is the fully connected Potts model exactly solvable?

Suppose that we have "spins" $\sigma_1,\dots,\sigma_N$, with $\sigma_i\in\{1,\dots,q\}$, for $i=1,\dots,N$, and that our Hamiltonian is $$ H = -\frac{J}{N} \sum_\stackrel{i,j=1}{i\ne j}^N \...
1
vote
0answers
25 views

What methods can I use to find the minimum of a tranverse field Ising model?

I am trying to solve for the minimum of the hamiltonian of the form: $$ H = \sum_{i,j} J_{ij}q(i)q(j) + g_i\sum_i x(i) $$ where q(i) is the operator (I + z(i))/2 and z(i) and x(i) are pauli operators ...
0
votes
0answers
11 views

What is the relationship between the Ising model and a magnet's corresponding magnetic field at varying temperatures?

I understand that ferromagnetism occurs when all the spins in a magnet are aligned, leading to the magnetic vector field that we are familiar with. What happens qualitatively to the magnetic field as ...
5
votes
0answers
78 views

Emergent supersymmetry in tricritical Ising model

In TASI Lectures on Emergence of Supersymmetry, Gauge Theory and String in Condensed Matter Systems there is a statement that 2d supersymmetry can can emerge from the dilute Ising model: $$ \beta H = ...
0
votes
2answers
45 views

Confusion about notation for block transformation in Ising model

I'm going through Cardy's "Scaling and Renormalization in Statistical Physics", and I've run across a notational confusion. Consider a 2D Ising system with the following Hamiltonian $$\...
2
votes
1answer
56 views

1D Ising Model: spin interaction in $z$-direction, magnetic field in $x$-direction

I've stumbled across an interesting extra question in an old exam. In my own words: Consider the Magnetization of the 1D Ising model $$H=-J\sum_iS_{z,i}S_{z,i+1}-B\sum_iS_{x,i}$$ at $T=0$. We know ...
2
votes
2answers
50 views

Relating scaling and critical exponents in the Ising model

I'm reading the chapter about the renormalization group in Yeoman's book "Statistical mechanics of phase transitions" and I'm puzzled about how the author relates the scaling of the RG with ...
0
votes
1answer
92 views

Boltzmann distribution in Ising model

I've written in Matlab a code for a Ising model in 1 dimension with 40 spins at $k_{B}T=1$. I record the energy of every step in a Metropolis Monte Carlo algorithm, and then I made an histogram like ...
1
vote
0answers
73 views

Relevant operators in Ising model

Why in 3d Ising near critical point there are only two relevant deformations? I am interested in experimental arguments and also in theoretical explanation. For example, in 3D Ising Model and ...
0
votes
0answers
30 views

A closer look on the derivation of the susceptibility in the Ising-Model

The susceptibility $\chi$ can be defined as $$ \chi = \frac{\partial \langle M \rangle}{\partial H}, \tag{1}$$ where $\langle M \rangle$ is defined as the average magnetization and thus can be written ...
0
votes
1answer
38 views

Ising model autocorrelation of magnetisation per state

I am trying to simulate Ising model, and have learnt that we get more accurate results when we take correlation time $\tau$ into account. I.e, decrease the correlations between observing samples only ...
1
vote
0answers
64 views

Ising spin are bosonic?

I was going through the following paper The 1D Ising model and the topological phase of the Kitaev chain. They call ising spins to be bosonic. If I the quote the paper: Hard-core bosons realized ...
1
vote
0answers
29 views

Correlation length for ising-Kitaev chain: Coincidence or are they same?

The correlation length for the two-dimensional classical ising model goes as $$\xi_{ising}(T)\sim |T-T_c|^{-\nu};\qquad \nu=1$$ We can map the classical ising model to its quantum cousin, one-...
0
votes
1answer
80 views

Value of critical exponent $\alpha$ for 2D ising model

The Onsager solution for specific heat is $$C\approx -Nk\frac{2}{\pi}\bigg(\frac{2J}{kT_c}\bigg)^2\ln\Big|1-\frac{T}{T_c} \Big|\qquad (T \textrm{ near } T_c)$$ Critical exponent $\alpha\neq 0$. ...
0
votes
1answer
48 views

Autocorrelation function problem in Monte Carlo simulation of 2D Ising model

Currently, I did a Monte Carlo simulation with the local update and Wolff cluster updated in 2D classical Ising model. I use the autocorrelation function to compare 2 different algorithm in critical ...
3
votes
1answer
104 views

Nonzero spontaneous magnetization in two-dimensional Ising model

The two-dimensional Ising model with the nearest-neighbour interactions enjoys a $\mathbb{Z}_2$ symmetry under $S_i\to -S_i$; it displays sponatebous symmetry breaking at a finite temperature $T_C=2J[...
1
vote
0answers
19 views

Applications of Sampling from SK Ising Model

I have written a program for Monte Carlo sampling from Sherrington-Kirkpatrick (SK) Ising model. I have two questions about it: 1- What are some applications of it? I already know training Boltzmann ...
1
vote
0answers
52 views

Simple Quantum Monte Carlo question

Currently I am doing some simple simulation of 1D Transverse field Ising model. I map the quantum mechanical problem into classical 2D classical Ising model with different horizontal interaction and ...
1
vote
0answers
69 views

Numerical renormalization of 2D Ising lattice

I'm trying to make some toy computations on the $2D$ Ising model on a square lattice. I want to apply a renormalization transformation, and try to estimate observables on the renormalized lattice ...
0
votes
2answers
85 views

What is the ground state wavefunction of $\hat{H}=-J\sum\limits_{\langle i,j\rangle}\hat{S}_i^z\hat{S}_j^z,~~ (J>0)$?

The hamiltonian of a collection of noninteracting quantum spin-$1/2$ operators $\hat{S}_i$ fixed at each lattice site $i(=1,2,..., N)$ in presence of magnetic field ${\bf B}=B\hat{{\bf z}}$ $$\hat{H}=-...
0
votes
2answers
53 views

Averages of absolute values in Monte Carlo simulation of Ising Model

Consider the 2D Ising model in $0$ field, with Hamiltonian $$ H=J\sum_{\langle i,j\rangle}\sigma_i\sigma_j$$ The magnetization per spin is defined as $$M=\frac{1}{N}\sum_i \sigma_i $$ Where $N$ is ...
1
vote
1answer
46 views

Needed Clarification: In Calculation of specific heat of Ising model (Simulation)

I am want to calculate the specific heat for 2D 100x100 square lattice ising model. I have calculated the correlation time, viz., $\tau$. Now I want to calculate the specific heat and error in ...

1
2 3 4 5
9