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425 views

Gaussian transformation for the Ising model (Hubbard-Stratonovich transformation) [closed]

I am currently about to understand the derivation of the Gaussian transformation of the Ising model, where i find the following step: $$Z= \sum_{\{s_i\}} e^{- \frac{\beta}{2} \sum_{i,j} J_{ij} s_i ...
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1answer
121 views

Periodic ground state 1-dim ising model

Good evening! I'm at the beginning of my study about the Ising model and it has been proposed to me this problem: Find all periodic ground-state configuration for the following one-dimensional Ising ...
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194 views

Why doesn't the 1 dimensional ising model have a transition temperature?

Consider a 1 dimensional chain of spins that are able to either have the value $\sigma =$ $+1$, $-1$, from now on referred to as up and down. For the Hamiltonian $H = J \sum_{i,j} \sigma_i \sigma_j$ ...
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59 views

Fluctuation-dissipation in a quantum Ising Model

For the classical Ising model, the fluctuation-dissipation theorem tells us that the Magnetic susceptibility is proportional to the variance of the magnetization. Is there an equivalent relation for ...
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0answers
136 views

Ising model. What is large fluctuations of magnetization?

My background is in mathematics. I have studied the Ising model in $\mathbb{Z}^2$. The main model of statistical mechanics. Yesterday, I was reading the preliminary notes of the book Statistical ...
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0answers
482 views

2D Ising model simulations: Wolff algorithm acceptance probability with an external magnetic field

I have implemented the Wolff algorithm to simulate a 2D ferromagnet. It works by building a cluster of like spins and flipping them all at once to move quickly through phase space. In the case of no ...
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0answers
40 views

Filling ising model with basis

This questions involves how to fill a lattice with ordered basis: Is there some established mathematical approach in filling a physical lattice with some colored basis (black and white here)? For ...
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0answers
74 views

Formula for the energy per site in the triangular Ising model

I'd like to check the correctness of a simulation I ran on the Ising model on a triangular by verifying if I get the good value of the mean energy per site. I found a formula giving it for high ...
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457 views

Is this a known entropy formula?

While playing around with a variant of the one-dimensional Ising model with periodic boundary conditions I came up with a formula, let's call it $F$, whose form looks suspiciously like an entropy ...
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1answer
533 views

Physical origins of the Heisenberg model of ferromagnetism

I am trying to understand physical intuition behind the Ising and Heisenberg models (thus I am not sure if my question is appropriate for this mostly mathematical site). I will concentrate of the ...
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1answer
94 views

Universality classes

I would like to ask about the universality classes. I know that these are the statistical models which describes different phase transitions with different critical exponents. But I would like to know ...
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1answer
78 views

Ising model scale invariance

Could someone help me and explain what is the connection between divergence of the correlation length, and the scale invariance. So why will in the critical point the system show scale invariance if ...
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3answers
389 views

How to calculate critical temperature of the Ising model?

Can someone name a paper or book which calculates the critical temperature of the Ising model from scratch? It might be a book and should contain the necessary prerequisites. I have had a basic course ...
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1answer
95 views

what's the world record in finding the ground state of the 3D Ising model

Finding the ground state of the 3D ising model (with no magnetization) is known to be NP-complete. Just wondering what is the biggest size cubic lattice someone has found the ground state of for this ...
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1answer
48 views

What is the length dimension in critical phenomena?

In this question it is said that: The best way to numerically work with continuous phase transitions is to study observables that have a vanishing length dimension (or mass dimension in the ...
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1answer
95 views

1D Ising model and degenerate states

I am studying the Ising model in 1D, in the absence of magnetic interaction but in presence of an external magnetic field. The Hamiltonian for an Ising chain with $n$ sites is hence described by $$H = ...
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1answer
260 views

How to calculate the exchange constant of the Ising model?

The Ising model is a mathematical model of ferro-magnetism in statistical mechanics. The model consists of discrete variables that represent magnetic dipole moments of atomic spins that can be in one ...
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0answers
15 views

Finite Temperature Signatures of QPT in the Transverse Ising Model

We know that in the transverse ising model $H=-J\sum_i\left(\sigma^x_i\sigma^x_{i+1}+g\sigma^z_i\right)$ there is a quantum phase transition right at the critical point $g=1$. I am wondering if ...
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8 views

What is the motivation behind defining short range order the way it is defined in Braggs-William approximation?

I am reading Statistical Mechanics by Kerson Huang. In the chapter on Ising model, it defines short range order as $\frac{2 N^{++}}{\gamma N}$ where $N^{++}$ is total number of spin up neighbours of ...
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0answers
103 views

Ising model at high vs. low temperature

The output of the Ising model over a 2D binary lattice looks to have spin states uniformly distributed over the lattice for high values of the temperature parameter with the output attaining ...
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1answer
29 views

Criticality and the number of paths on a lattice

In the review "Scaling, universality, and renormalization: Three pillars of modern critical phenomena" by Stanley, he makes the following claim towards the end of the paper, which is neither derived ...
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0answers
19 views

Swendsen Wang different implementations

I have recently a confusion about the different adding probabilities of bonds in the Swendsen Wang cluster algorithms with e.g. application to the Ising or Potts model. In literature there are ...
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0answers
17 views

Good broad review of agent-based modeling?

Trying to find some good review of agent-based models and networks, covering opinion dynamics, correlated behavior, phase transition analogies, etc. Are there any articles or books that cover major ...
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0answers
76 views

Mean-field solution of Potts model

The mean-field equation for the three-state Potts model $H= -J∑δσiδσj$ can be derived as follows using this: a) show that $H$ is equivalent to $-J∑Si.Sj$ where, $Si=(1 0) , (-1/2 √3/2 ) , (-1/2 ...
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0answers
80 views

Problem in deriving the second term in perturbation expansion the quantum ising model

So I'm trying to derive the perturbation expansion for one particle states in the quantum ising model (Sachdev 2011 QPTs which this is derived from ) $$ H_I= - J g \sum_i \sigma_i^x - J \sum_{\langle ...
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0answers
41 views

What do physicists mean with “classical critical behaviour”?

What do physicists mean with "classical critical behaviour"? As far as I am concerned it should be "power law behaviour" of some quantity close to the critical point but I ask here to be sure.
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37 views

How to interpret a null critical exponent?

In the 2D Ising model the value for $\alpha$ is $0$, but I fail to see how we can have this if the specific heat of the system actually has a divergence in the critical temperature. I've seen this ...
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1answer
129 views

Topological entanglement entropy in transverse quantum Ising model?

I have seen from literature that the $Z_2$ lattice gauge theory in 2d could be mapped into a quantum Ising model with gauge constraints on the Hilbert space by dual transformation. The deconfined ...
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1answer
184 views

Ising model with metropolis algorithm around critical temperature

I'm trying to simulate Ising model using metropolis algorithm. Boundary conditions are periodic. I know how the algorithm works and I have written the code myself. Everything works as it should except ...
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0answers
292 views

Magnetic susceptibility in ising model as magnetization change

Let's say I have a standard 2D Ising model with $$ H(\sigma) = - \sum_{<i~j>}\sigma_i \sigma_j - h\sum_{j} \sigma_j $$ With the metropolis algorithm, I can compute various things like energy ...
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0answers
73 views

Ising Model 2D Correlation Length

I'm using Metropolis and Wolff Clustering algorithms to estimate the spin-spin correlation function $$<s_os_r>$$ I know that this is related to the correlation length but how do we determine ...
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0answers
62 views

Ising Model with All Spins Interacting with All Other Spins

I am studying the Ising model with all spins interacting with all other spins and have formulated $Z$. I am trying to understand what it means to study at large N but not infinite N. I know that at ...
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0answers
55 views

Why isn't the 3 pts function vanishing in the Ising model by Z_2 symmetry?

The Ising model with vanishing external field possesses the $Z_2$ symmetry: $$\sigma_i \rightarrow - \sigma_i$$ implying that the 1 pt function vanishes: $$<\sigma_i> \;= 0$$ In the same ...
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2answers
68 views

Minimization of energy for non-equilibrium systems at steady state (NESS)?

Suppose a non-equilibrium system at steady state. Does the steady state corresponds to the state of some minimal "energy-like", like in classical statistical physics? Example with the Ising model. ...