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 ...

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2-D Ising model temperature of equilibrium [duplicate]

I have simulated 2-D Ising model in C#, but my scatter plot for magnetization versus temperature is an decreasing line (you know that the correct plot decreases quickly in a temperature near 2.3). ...
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42 views

Majorara zero mode in Ising chain, not exactly zero subtlety

We know the transverse field Ising model with N sites(open boundary), can be mapped into N free fermions(there are 2N modes if including the negative energy counterparts) With property: ...
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42 views

2d Ising model simulation [on hold]

I have written following code for simulating 2d 'ising' model, code is in c# console and you can run it easily. my problem is that by increasing temperature, magnetization and energy don't change and ...
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1answer
46 views

Can particle quantum spin be described with a wave function? [closed]

I'm a little confused about the idea of spin. It's been non-technically described to me as "like magnetic dipole moment", except only two possible "directions". But I feel like that's a bad analogy, ...
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37 views

Intuition on Gibbs measures

I am (roughly) aware of the way Gibbs measures are used to solve physical systems (e.g. the Ising model). We can basically boil it down to pinpointing a Hamiltonian. My question is, consider a ...
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16 views

Application of the Mean Field Approximation for molecules

When I studied the Ising Model in a course on Statistical Physics one approach that was presented was to use the Mean Field Approximation. In the ocasion I've noticed that it is also called "molecular ...
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34 views

Decimation of a triangular lattice [closed]

Consider the network of spins shown below. The Hamiltonian is given by $$H = - \sum_{\langle i j k \rangle} [J \sigma_i \sigma_j \sigma_k + J_0]$$ with $J,J_o \geq 0$ and $\langle i j k \rangle$ ...
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1answer
179 views

Temperature in the Hamiltonian limit

There is a well known connection between statistical mechanics in D spatial dimensions and quantum field theory in D-1 spatial dimensions. Changing the temperature in statistical mechanics corresponds ...
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1answer
143 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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23 views

Phase transition in mean field theory Ising model

For the Ising model mean field theory is supposed to give quantitatively correct answers in dimensions>=4. I have written code to compare the results of mean field theory to a 4D or 5D Ising model and ...
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31 views

Ising model as quantum model?

I've read in a few papers things that use the fact that the $2D$ Ising model can be interpreted as a $1+1$ quantum spin model. I haven't been able to find this description and would like to read about ...
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3answers
120 views

What is the difference between toy models and normal models? [closed]

Here is the short description of scientific model: an imperfect or idealized representation of a physical system And the definition of toy model: a simplified set of objects and equations ...
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127 views

What is the momentum canonically conjugate to spin in QM?

In Kopec and Usadel's Phys. Rev. Lett. 78.1988, a spin glass Hamiltonian is introduced in the form: $$ H = \frac{\Delta}{2}\sum_i \Pi^2_i - \sum_{i<j}J_{ij}\sigma_i \sigma_j, $$ where the ...
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1answer
46 views

Applicability of Cardy's “doubling trick” to the 2D Ising Model

In Section 11.2.2 of the book on Conformal Field Theory by di Francesco, Mathieu, and Senechal (page 417), the two point function on the Upper Half Plane is written as being equal to the four point ...
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69 views

Transfer from Heisenberg to Ising model

It is well know, that ferromagnets can be described using Hamiltonian $$ H = -\sum\limits_{i<j}J_{ij}\, (\mathbf{s}_i \cdot \mathbf{s}_j). $$ where (three dimensional) spins $\mathbf{s}_i$ ...
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1answer
210 views

What are alternative ways to think about transfer matrix as used in Ising model?

I recently learned about how to find the partition function of Ising model using Transfer Matrix method. At my level of understanding things, it is a trick that happens to work! I would like to ...
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2answers
124 views

Time reversal symmetry of transverse field Ising model

Is the transverse field Ising model time-reversal invariant? Specifically consider a non-integrable variant: \begin{equation} H = -J \sum_i^{L-1} \sigma_i^z \sigma_{i+1}^z + g \sum_i^L \sigma_i^x + h ...
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1answer
4k views

Force from solenoid

I'd like to approximate the force from a solenoid, or at the very least find a formula which is proportional to the force so that I can experimentally find the constant for my particular case. ...
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31 views

Majorana fermions and the continuum limit of the Ising model

In Paolo Moligini's Analyzing the two dimensional Ising model with conformal field theory lecture notes, it is shown at the end of chapter 3 that the Lagrangian of the continuum limit of the Ising ...
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3answers
73 views

If an Ising model is in contact with two thermal reservoirs, would it still experience a phase transition if one of the reservoirs is below Tc?

For example; Two reservoirs are at each end of a one dimensional or even two dimensional lattice. One of the reservoirs has the temperature T < Tc. Would the lattice site have a phase transition ...
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84 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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236 views

Is there a spin glass version of Prince Rupert's Drop?

Spin Glasses are known to converge to their ground state under Simulated Annealing. The word choice is especially interesting since annealing is also the name of a process performed on actual glass. ...
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2answers
73 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. ...
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18 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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11 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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69 views

${\phi}^4$ description of Ising ferromagnet

Suppose the coupling between two spins is $C_{i,j}<0$, then the classical partition function is given by $$Z=\sum_{\{s_i\}}e^{\sum_{i,j}s_iK_{ij}s_j+h\sum_{i}s_i}$$ where $K_{ij}=-\beta C_{ij}$ and ...
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40 views

Thermodynamics for 1D line of 3D dipoles

The 1D Ising model was solved almost a century ago. This model assumed spins that point along the 1D line to the left or right and only considered nearest neighbors, so that the Hamiltonian with no ...
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111 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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2answers
473 views

Renormalization Group and Ising with d=1 and D=1 [closed]

I have a question about the results of RG on Ising model. I know it's possible to obtain two couple of relations $K'(K)$, $q(K')$ $K(K')$, $q(K)$ between the coupling costants. My problem arise ...
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1answer
30 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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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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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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1answer
150 views

Critical temperature and lattice size with the Wolff algorithm for 2d Ising model

When I run my implementation of the Wolff algorithm on the square Ising model at the theoretical critical temperature I get subcritical behaviour. The lattice primarily just oscillates between mostly ...
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1answer
82 views

Finite temperature transverse magnetization in transverse Ising model

Consider the transverse field Ising model, with $H=-J\sum_i\left(\sigma^x_i\sigma^x_{i+1}+g\sigma^z_i\right)$ What happens to the expectation value of the magnetization $\langle\sigma_z\rangle$ at ...
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1answer
283 views

Local minima in Ising model in a Monte Carlo simulation

Is there any way to check whether in a Monte Carlo simulation using Ising model is stuck in any (false) local minima of energy or not, particularly in 3D system ?
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153 views

What real experimental systems are well-described by Glauber-Ising spins?

I'm hoping for references to actual physical systems in which all or at least most of the following can be simultaneously characterized: the spin flip rate, the temperature, and a relaxation or ...
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2answers
177 views

Phase transition without the Peierls' counter argument

Is there any proof of the existence of phase transition in models of statistical mechanics of the Ising type models without using the Peierls' argument and its variations? By models of the Ising ...
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103 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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1answer
112 views

Ising model on lattices with (vertical side length) $\neq$ (horizontal side length)

Consider the Ising model with nearest neighbours interactions on a rectangular lattice $L\times M$. If $L=M$ (2-dimensional square lattice), it is known (e.g. by Peierls argument or Onsager explicit ...
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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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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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0answers
48 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
241 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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1answer
146 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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92 views

Mixed spin Ising Model

As we know ferrimagnets can be modeled by the Ising model. I came across this equation in "Compensation Temperature of the Mixed-Spin Ising Model on the Hexagonal Lattice" by W. Figueiredo, M. Godoy, ...
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127 views

Construction of free energy based on Landau theory

Consider an Ising model system where the total energy is $E = −J \sum_{<ij>} S_iS_j $, $S_i = \pm 1$ and $< ij >$ implies sum over nearest neighbours. For $J < 0$ the ground state of ...
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1answer
436 views

How does Metropolis algorithm work in the Ising model?

I was reading the proof of Metropolis algorithm. The transition probability of going from a state $i$ to a state $j$ is $\pi_{ij}$. If I understand correctly, this is the product $\pi_{i ...
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1answer
109 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
88 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 ...
0
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1answer
111 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 = ...