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
0
votes
1answer
75 views

$\nabla E=0$ in $2$D Ising model - accept or not?

2D Ising model simulation using Metropolis algorithm. There is one thing which I don't understand. The difference in energy $\Delta E$ between initial state and new state is: $\Delta E = 2Js\...
1
vote
1answer
919 views

Measuring correlation lengths of 2D Ising model by Monte Carlo simulation?

I want to measure cluster size and cluster number at different temperatures below and above critical temperature in 2d Ising model by Monte Carlo method. In other words, I must measure correlation ...
0
votes
1answer
345 views

Factor two in partition function derivation (1D Ising model)

In the derivation of the Ising model at zero field $B=0$, I stumbled upon a factor two in the textbook derivation that I don't understand. We consider a 1D system of interacting spins $s_i$, where $i$...
1
vote
0answers
136 views

What is the anomalous dimension for two-dimensional multi-component spin systems?

My question is: What is the (predicted) anomalous dimension $\eta$ for the two-dimensional $n$-vector model (or $O(n)$ model)? Note: I am not looking for a derivation of $\eta$. A simple reference to ...
0
votes
1answer
82 views

Ising model with fixed length [duplicate]

Someone made the comment for an Ising model that: When finite length is fixed for a rectangular Ising model, there still is no phase transition. How do they know this? EDIT: To make the ...
1
vote
0answers
509 views

Calculating partition function of the Ising Model [closed]

I have that the energy of my model is such that every spin interact with each other: \begin{equation} E = -\frac{J}{2N}\left(\sum_{i}\sigma_i \right)^2 - h\sum_i\sigma_i \end{equation} And I have to ...
2
votes
0answers
113 views

Finding recursion relation in renormalization group theory

I'm trying to learn statistical mechanics by studying the book by Plischke and Bergersen, but I'm stuck with how to find the recursion relation (which can be used to find the fixed points) in ...
0
votes
1answer
55 views

Ginibre inequality in Aizenman & Simon paper

In the paper linked below equation (4) is not well justified. After a lot of reasoning I still can't figure out why the need of taking the hamiltonian in the H' form and how should I use Ginibre ...
3
votes
0answers
595 views

A question in Quantum Phase Transition of Transverse Ising Model

In section 1.4 quantum Ising model of Subir Sachdev's book Quantum Phase Transitions, he discusses the quantum phase transition of transverse quantum Ising Model at zero temperature (so we just focus ...
1
vote
1answer
115 views

Mathematical identity in equation (3.7) of John Cardy's Scaling and Renormalization

I know I'm at risk of appearing quite stupid, but can someone explain to me the following identity, appearing in equation 3.7 of Cardy's book. $$ e^{Ks_3s_4} = \cosh(K)(1 + \tanh(K) s_3s_4) \tag{3.7} ...
4
votes
2answers
261 views

Why symmetry breaking?

Let me elaborate the question by using 2D Ising model without external magnetic field. When we lower the temperature and pass $T_c$ a little bit, the theory of spontaneous symmetry breaking tells us ...
1
vote
0answers
100 views

General Ising model

I have a specific Ising model Hamiltonian for a tetrahedral unit cell looks like: $$ H= J1 (S_1^zS^z_2 + S_1^zS^z_3 +S_1^zS^z_4 +S_2^zS^z_3+S_2^zS^z_4+S_3^zS^z_4) -2*J2(S_1^xS_2^x+S_1^yS_2^y+...
2
votes
1answer
347 views

What is the lower critical dimension (LCD) of the bond-diluted Ising model?

It is known that the lower critical dimension (LCD) $d_l$ of the Ising model is $d_l=1$, that the LCD of the Edwards-Anderson model is $d_l=5/2$ (source) and that the LCD of the random field Ising ...
3
votes
1answer
337 views

Non-homogeneous Ising model in one dimension

In formula of Hamiltonian for Ising model in one dimension we have $J_{ij}$. usually, we take $J_{ij}$ as a constant. In this way it is called homogeneous Ising model. My question is if we take $J_{...
4
votes
1answer
3k views

Why do spin correlation functions in Ising Models decay exponentially below the critical temperature?

I'm trying to form a better understanding of the 2D Ising Model, in particular the behaviour of the correlation functions between spins of distance $r$. I've found a number of explanatory texts that ...
6
votes
1answer
223 views

Zero modes $a_j\sim e^{-\kappa j}$ in a semi-infinite quantum Ising chain?

As a way of analyzing the performance of quantum annealing, I've been studying quantum diffusion in fermionizable lattice models with zero modes. In particular, the 1+1D quantum Ising model, semi-...
3
votes
0answers
151 views

Ising CFT on a higher genus surface

I'm wondering if someone knows how to put the critical Ising model on an arbitrary Riemann surface of genus g. I know how to do it on a torus but I want to know how to find the correlator of the Ising ...
5
votes
1answer
180 views

A question about the two-dimensional Ising model

The two dimensional square lattice Ising model reads $$E[\sigma]=-J\displaystyle\sum_{<ij>}\sigma_i\sigma_j-h\displaystyle\sum_i\sigma_i,$$ where $E$ is the energy, $\sigma_i$ is the spin at ...
10
votes
2answers
725 views

What new features does the Heisenberg Model have compared to the Ising Model?

Both the Ising and the Heisenberg Models describe spin lattices with interaction on first neighbors. The Hamiltonian in each case is quite similar, despite the fact of treating de spins as Ising ...
4
votes
2answers
2k views

Why correlation length diverges at critical point?

I want to ask about the behavior near critical point. Let me take an example of ferromagnet. At $T < T_c$, all spins are aligned to the same direction thus it is in the ordered state, scale ...
3
votes
1answer
3k views

What is the difference between classical and quantum Ising model?

The Ising model is defined with the Hamiltonian: $$ H = -\sum_{<i,j>}S_i^z\cdot S_j^z $$ What is the difference between quantum version and classical version? My intuition is that the ...
0
votes
1answer
104 views

Ising simulation-dimensionless

My question is about dimensions in Ising model.When we want to simulate Ising we use dimensionless parameter as you know.We choose J to be 1 and also K equal 1 and when temperature is 2.26 then it's ...
0
votes
1answer
145 views

Intuition for defining basis for Hamiltonian in momentum representation

I am going through Quantum information approach to the Ising model: Entanglement in chains of qubits by Stelmachovic et al. In Section A.4, the authors determines the eigenvalues and eigenstates of ...
1
vote
0answers
446 views

Exact Solution of Ising Model in Open Boundary condition

What will be the exact expression of the partition function for 1d Ising model, if we consider open boundary case (This implies that the last spin in the sequence does not interact with the first spin)...
1
vote
0answers
42 views

Why do the singularities of the thermodynamic functions expected to be non-negative powers?

I am going through the first chapter of Exactly Solved Models in Statistical Mechanics. On page 4, at the end of section 1.1 it is said that: I would like to know the basis of this expectation. ...
6
votes
1answer
418 views

Wick's theorem and transverse field Ising model

I am trying to understand calculation of correlation function in the ground state of the Transverse Field Ising model, from the following book, which is freely available: http://link.springer.com/book/...
1
vote
0answers
74 views

Master curve of the 3D Ising model

I am currently doing some grand canonical Monte Carlo simulations for LJ particles and my professor has asked me to map the normalized probability distribution of density on to a master curve of the ...
3
votes
0answers
151 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: $$\gamma^\...
1
vote
1answer
614 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, ...
2
votes
0answers
112 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 ...
2
votes
0answers
76 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 $\langle i j k \rangle$ ...
3
votes
1answer
215 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 ...
1
vote
1answer
202 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 ...
3
votes
0answers
564 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 $\mathbf{s}_i$ ...
16
votes
2answers
663 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 ...
6
votes
2answers
838 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 ...
1
vote
0answers
249 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 ...
1
vote
3answers
123 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 ...
1
vote
3answers
1k 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 ...
0
votes
2answers
128 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. ...
10
votes
1answer
805 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 ...
4
votes
1answer
495 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 ...
2
votes
0answers
58 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 ...
8
votes
1answer
598 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 ...
2
votes
0answers
275 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 ...
0
votes
1answer
58 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 ...
5
votes
1answer
1k 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 ...
1
vote
2answers
305 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 type ...
0
votes
1answer
63 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 ...
0
votes
0answers
263 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 ...