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3answers
247 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 ...
0
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1answer
355 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 ...
2
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0answers
93 views

Motivation of the Heisenberg model of ferromagnetism

In the Heisenberg model of ferromagnetism the atoms are assumed to be arranged in a lattice. The $i$-th atom has a spin operator $\vec S_i$ (here $i$ belongs to the lattice). The Hamiltonian is given ...
5
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1answer
388 views

Interpretation of the 1D transverve field Ising model vacuum state in a spin-language

The 1D transverse field Ising model, \begin{equation} H=-J\sum_{i}\sigma_i^z\sigma_{i+1}^z-h\sum_{i}\sigma^x_i, \end{equation} can be solved via the Jordan-Wigner (JW) transformation (for further ...
3
votes
1answer
86 views

Explicit definition of the energy operator in the Ising model

I've simulated a few 2d Ising models at critical temperature on triangular lattice and I'm now trying to check that the correlation functions are right. I alraedy did it for the spin operator ...
5
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1answer
152 views

Ising model for ferromagnetism is not intuitive

In the Ising model for ferromagnetism a lower energy is assumed when two spin magnetic dipoles are aligned parallel to each other and the energy is higher when they are antiparallel. If I take two ...
0
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1answer
85 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 ...
4
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0answers
114 views

Spin Glass Prince Rupert's Drop

Spin Glass is known to converge to its ground state under Simulated Annealing. The word choice is especially interesting since annealing is also the name of a process performed on actual glass. ...
0
votes
1answer
141 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 ...
3
votes
1answer
569 views

1D Ising Model (NN and NNN interactions) with 2 transfer matrices

I've tried an alternative solution for finding the partition function of this model. So is what I've done correct? If it isn't then please prove and explain why not. (I'm pretty sure I made a ...
0
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0answers
53 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 ...
0
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0answers
327 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 ...
1
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0answers
37 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 ...
1
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0answers
70 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 ...
4
votes
2answers
330 views

Mean field theory = large-N approximation?

Wikipedia entry of 1/N expansion (or 't Hooft large-N expansion) mentions that It (large-N) is also extensively used in condensed matter physics where it can be used to provide a rigorous basis ...
3
votes
1answer
187 views

Percolation and number of phases in the 2D Ising model

Update. As my previous figure had conceptual mistakes I decided to change the picture to another, more instructive. After a long time I came back to try to understand an article on the Ising model. ...
1
vote
1answer
174 views

detailed balance in the context of the ising model

I am having a very basic problem understanding the idea of detailed balance, particularly in the context of the Ising model. Most references I have found contain the following phrase: "In ...
1
vote
2answers
134 views

Is it possible to find the ground state of generalized Ising models?

Is there a general solver (or a theoretical algorithm) for obtaining the ground state configuration of the extended Ising model, which involves an arbitrary lattice, arbitrary coordination number ...
2
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1answer
166 views

Research on ground state configuration of Ising model

I want to do mathematical research (algorithm construction and mathematical analysis) on Ising model ground state configuration. From what I know, the state of art research is using graph theory ...
1
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2answers
585 views

Acceptance probability 2D Ising Model

Disclaimer: I just found a possible solution - eventhough i don't really understand, whats wrong with my prior approach. Edit: I just tried to calculate it from scratch and found the following: $E ...
3
votes
1answer
780 views

Some limiting cases of the Heisenberg XXZ model (2/2)

NOTE: Because this was a long question I have split it up in two different questions! For a course on quantum integrability I am reading these notes. (Franchini: Notes on Bethe Ansatz Techniques. ...
1
vote
1answer
461 views

Some limiting cases of the Heisenberg XXZ model (1/2)

NOTE: Because this was a long question I have split it up in two different questions! For a course on quantum integrability I am reading these notes. (Franchini: Notes on Bethe Ansatz Techniques. ...
2
votes
1answer
212 views

Ising model Mean field theory and translational invariance

In the Ising model the mean value of any particular spin is: $$ m = \left<s_i\right> = \frac{ \sum_{s_i}e^{-\frac{H}{T} }s_i} { \sum_{s_i} e^{-\frac{H}{T} } } .$$ I read in several ...
1
vote
1answer
186 views

Infinite-range 1D Ising model

The Hamiltonian for this system is given by \begin{equation} \mathcal{H} \{S\} = -H\sum_i S_i - \frac{J_0}{2} \sum_{ij} S_i S_j, \end{equation} where $H$ is the external magnetic field and there is no ...
3
votes
2answers
557 views

1D Ising Model with different boundary conditions

The Hamiltonian for one-dimensional Ising model is given by, \begin{equation} \mathcal{H} = -J\sum_{<ij>} S_iS_j; \quad i,j=1,2,...,N+1 \end{equation} where $<ij>$ denotes that there is ...
5
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2answers
258 views

Ising model observables

Is there a formula or equation relating $\langle E\rangle$ and $\langle M\rangle$ (average spin per site) and $\langle E^2\rangle$ to temperature $T$ for the square lattice Ising model at zero ...
2
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0answers
113 views

How to use Ising Spin model for prediction of time series “Phase”

I am investigating a 2d Ising Spin Lattice. I have been able to generate a Monte Carlo app that gives me the changing spin matrix through my iterations - like the many examples on the web. However, ...
1
vote
2answers
618 views

1 dimensional Ising model

How to solve the Ising model in 1D by low temperature, and high temperature expansion, and by change of variable method? Can you please give me some reference links?
1
vote
1answer
470 views

Ising spin vs Pauli spin matrices

Are Ising spins scalar or operators? I am not a condensed matter physicist hence having some confusion. I have learnt about Ising models from adiabatic quantum algorithm papers. For example this ...
2
votes
1answer
266 views

NP-completeness of non-planar Ising model versus polynomial time eigenvalue algorithms

From the papers by Barahona and Istrail I understand that a combinatorial approach is followed to prove the NP-completeness of non-planar Ising models. Basic idea is non-planarity here. On the other ...
3
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0answers
104 views

Monte Carlo for Random Bond Ising ferromagnet

The set-up: Consider the Ising model on an $L \times L$ square lattice, where the coupling of each bond is chosen to be $+J$ (ferromagnetic) with probability $(1-p)$ and $-J$ (antiferromagnetic) with ...
2
votes
1answer
43 views

Does an Ising lattice that returns to equilibrium create a current by induction?

Consider you have an Ising lattice with a dominant up component out of thermal equilibrium, that's your initial state. The down spins want to flip up and align with the ups, and they'll do so until a ...
2
votes
1answer
211 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 ?
5
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2answers
5k views

What is the definition of correlation length for the Ising model?

The correlation length $\xi$ is related to critical temperature $T_c$ as $$ \xi\sim|T-T_{c}|{}^{-\nu}, $$ where $\nu$ is the critical exponent. Is this the formal definition of correlation ...
4
votes
1answer
667 views

A simple model that exhibits emergent symmetry?

In a previous question Emergent symmetries I asked, Prof.LuboŇ° Motl said that emergent symmetries are never exact. But I wonder whether the following example is an counterexample that has exact ...
4
votes
2answers
100 views

Determining the probability of a particular site having a particular spin in an Ising model

Given an Ising model, we have the energy formula: $E= - \sum_i h_i S_i - \sum_{i \neq j} J_{ij} S_i S_j$ and we have the probability of a given state, given the energy of that state and the ...
3
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3answers
351 views

Results of Statistical Mechanics first obtained by formal mathematical methods

I have a question that seems natural in Physics and Mathematics mainly in Statistical Mechanics of Equilibrium. Results that are proven by formal mathematical methods that were already seem intuitive ...
2
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0answers
206 views

Spontaneous symmetry breaking in the quantum 1D XX model?

The ground states of the quantum 1D Ising and Heisenberg models exhibit spontaneous magnetization. Is this also true for the 1D XX model?
5
votes
2answers
239 views

Toric Code and Random Bond Ising Model

It was established by Dennis, Kitaev et al. that the 2D Toric Code can be mapped to a 2D Random Bond Ising Model. The original derivation was given in the paper "Topological quantum memory" which ...
5
votes
2answers
414 views

Renormalization Group and Ising with d=1 and D=1

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 ...
3
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0answers
73 views

Question about the derivation of an equation in full replica symmetry breaking solution

Using replica method and saddle point method, the free energy of a magnetic system can be expressed as $$-\beta[f]=\lim_{n\to0}\{\frac{-\beta^2J^2}{4n}\sum_{a\ne b}q_{\alpha\beta}^2-\frac{\beta ...
2
votes
0answers
102 views

Spin Glass Transitions in Random Bond Ising Model (RBIM)

In brief, is there a list of spin glass transition properties for the RBIM on different lattices? Is there any know results about the relationships between these probabilities for a graph and its ...
3
votes
3answers
654 views

Ising Ferromagnet: Spontaneous symmetry breaking or not?

In explaining/introducing second-order phase transition using Ising system as an example, it is shown via mean-field theory that there are two magnetized phases below the critical temperature. This ...
3
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1answer
104 views

Freedom in the Choice of a Beta Functions in RG

Assume we're given a certain statistical model, say the infinite range Ising model \begin{equation} H_{N}\{\vec\sigma_{N}\}~=~ - \frac{x_{N}}{2N} \sum_{i,j =1}^{N} \sigma_{i} \sigma_{j} ...
5
votes
1answer
307 views

The strong Markov property of Gibbs measures in 2D Ising Model

My background is that of a mathematician. I have a question about the two Dimensional Ising Model. I think the terminology I use is similar to the physical. I'm trying to understand the following ...
2
votes
4answers
199 views

What is the simplest system that has both, discontinous and continous phase transitions?

I am looking the simplest system that has both discontinous phase transition and a continous phase transition between the same phases (you can change one parameter). discontinous transition: first ...
6
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1answer
582 views

Mean-field theory in 1D Ising model

A mean-field theory approach to the Ising-model gives a critical temperature $k_B T_C = q J$, where $q$ is the number of nearest neighbours and $J$ is the interaction in the Ising Hamiltonian. Setting ...
5
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1answer
536 views

Percolation in a 2D Ising model

For a 2D Ising model with zero applied field, it seems logical to me that the phases above and below T_c will have different percolation behaviour. I would expect that percolation occurs (and hence ...
9
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0answers
164 views

Measure of Lee-Yang zeros

Consider a statistical mechanical system (say the 1D Ising model) on a finite lattice of size $N$, and call the corresponding partition function (as a function of, say, real temperature and real ...
2
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1answer
119 views

What's the meaning of the coupling change after a renormalization (in the 1-dim Ising Model)?

What does it mean that after the theory (1-dim Ising model here, but the question is general) is renormalized one time and $g_i\rightarrow g_i'$, that the couplings are weaker, even if the theory ...