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2
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1answer
166 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. ...
2
votes
1answer
231 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 ...
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
118 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 ...
2
votes
2answers
322 views

Identifying a critical phenomena?

I have a system with a number of measurables (in time). Some measurables are discrete some are continuous (within the measurement accuracy). How can I determine whether my system experiences ...
2
votes
1answer
62 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 ...
2
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0answers
44 views

Is there a reasonable lower bound for free energy per site of the 2D Ising model in the presence of an external field?

Given the standard Ising partition function: $$Z(\theta ,h) = \sum\limits_{\bf{x}} {\exp \left\{ {\theta \sum\limits_{(i,j) \in E} {{x_i}{x_j}} + h\sum\limits_{i \in V} {{x_i}} } \right\}}, $$ is ...
2
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0answers
82 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 ...
2
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0answers
98 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, ...
2
votes
0answers
184 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?
2
votes
0answers
99 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 ...
1
vote
1answer
132 views

I'm getting weird autocorrelations when simulating an Ising model below the critical temperature

So I'm simulating an Ising model using Monte Carlo and the Metropolis algorithm. After letting it reach equilibrium, I try to calculate the autocorrelation of the magnetization. As long as the system ...
1
vote
2answers
128 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 ...
1
vote
2answers
444 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 ...
1
vote
1answer
117 views

How to calculate the ground-state energy for the Ising model?

I'm learning about the 2D ferromagnetic Ising model in zero field and trying to verify what I know by calculating the ground-state energy for the state with all 'up' spins in a 3x3 lattice. $$H = ...
1
vote
1answer
70 views

Describe Ising model dynamics in stochastic differential equation or stochastic process

The Ising model is described by the Hamiltonian $$ H(\sigma) = - \sum_{<i~j>} J_{ij} \sigma_i \sigma_j -\mu \sum_{j} h_j\sigma_j, $$ and is treated extensively by equilibrium statistical ...
1
vote
1answer
62 views

Why we never observe superposition of up and down ferromagnetic ground state of Ising model?

I thought it is due to spontaneous symmetry breaking. But isn't that because we never observe the superposition states, then we claim that there is spontaneous symmetry breaking. It looks like ...
1
vote
1answer
438 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. ...
1
vote
1answer
159 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 ...
1
vote
2answers
528 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
418 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 ...
1
vote
1answer
54 views

Ising model 2-dimensional - ground state configuration

I have to prove something about the 2-dimensional ising model. The problem is the following: Prove that every nearest-neighbour and next-nearest-neighbour interaction on the square lattice ...
1
vote
1answer
65 views

How is free energy built into a Metropolis Monte Carlo simulation of an Ising model?

In the Metropolis algorithm, the change in the energy given by the hamiltonian is compared for flipping a spin. This is not the free energy, but for systems above absolute zero you are trying to ...
1
vote
1answer
31 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 ...
1
vote
0answers
70 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 $H = J \sum_{i,j} \sigma_i \sigma_j$ ...
1
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0answers
27 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 ...
1
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0answers
84 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 ...
1
vote
1answer
405 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. ...
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
vote
0answers
64 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 ...
1
vote
1answer
131 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
0answers
435 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 ...
0
votes
1answer
288 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 ...
0
votes
3answers
190 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
votes
1answer
80 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 ...
0
votes
1answer
116 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 ...
0
votes
0answers
37 views

A question about Ising model

If $H$ is the Hamiltonian of an Ising model of $n$ spins on a lattice then is the following quantity look like something one has seen? $([uI-H]^{-1})_{ii} - \frac{1}{n}Tr[[uI - H]^{-1}]$ where $u$ ...
0
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0answers
17 views

Is getting the ground state of Edwards-Anderson model NP hard?

I know 1D and 2D Ising model has a general solution. And I also know getting the ground state of 2D Ising model with transverse field and 3D Ising model is NP-hard.[Onsager][Barahona] So my question ...
0
votes
0answers
18 views

Ising Monte-Carlo and Three point functions

I'm looking for literature on the calculation of three points function in the 2d Ising Model using numerical methods, especially around the critical point. By $Z_2$ symmetry, three spin insertions is ...
0
votes
0answers
35 views

How to calculate the partial entropy in a fully connected ising system

I'm trying to reproduce a calculation that should lead to the partial entropy in a fully connected ising model for the high-temperature range ($\beta < 2$) in the thermodynamic Limit ($N ...
0
votes
0answers
36 views

Wolff vs Swendsen Wang Algorithm

Following the orginal paper of Swendsen Wang, their dynamical critical exponent $z$ is about $z=0.35$, whereas the Wolff Algorithm seems to have $z=1.19$. When I calculate the Correlation time though, ...
0
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0answers
37 views

Ising formulation of the graph isomorphism problem

Context I have been going through Ising formulations of many NP problems by Andrew Lucas. In section 9 on page 22, the author gave an Ising formulation of the graph isomorphism problem. Here I ...
0
votes
0answers
25 views

Generalization of a spin-glass order parameter definition

I am going through the paper, Solving the graph-isomorphism problem with a quantum annealer, by Hen et. al. Equation 4 on the second page gives the definition of the spin-glass order parameter as ...
0
votes
0answers
52 views

Find the lowest excitation of a given Hamiltonian

Is there a standard way to find the lowest excitation energy of given Hamiltonian without knowing the eigenstates? In particular I have the find the lowest excitations of an 1D Ising Hamiltonian in 1D ...
0
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0answers
52 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
votes
0answers
214 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 ...