Ising model Definition and 89 Threads

In the well known Ising model, without any external field (H=0), the energy (E), spins (s) and exchange interaction (J) are related as in the following equation $$ E = -\sum_{<ij>}J_{ij}s_{i}s_{j} $$ Jij is site dependent and consists of three components JAA, JBB and JABwhere A is say up...

I've been reading through some of the literature on solutions of the Ising model, but I can't help but notice it doesn't provide that good a model for actual ferromagnetic systems. It seems that these models get a lot of attention and I'm just curious as to why? Also, why is an exact solution to...

I'm currently working on a project for a code that does umbrella sampling of a 2-D Ising model [size LxL of a magnet (analyzing up or down spins)]. The next step is to take my code to analyze a nucleation region and its growth by varying the temperature above critical. Before I even attempt to...

Why in case of Ising model ##H=-J\sum S_iS_{i+1}## we calculate canonical partition function?

Energy function ##E=-S_1S_2##. I took ##J=1##. If spin are oriented parallel energy is negative. How could energy be negative?

is it possible to use renormalization group theory to get the critical temperature of the 2d ising model? or even, is it possible to show that there is a critical point?

is there any reference on ising model i would like to see all the exact results on ising model for 2d ising model, the correlation length diverge as t to -1 around the critical temperature how is this result derived?

Homework Statement Calculate magnetisation for partition function ##Z=12+4\cosh (8\beta J)## for Ising model 2x2 lattice.Homework Equations F=-k_BTln Z M(H,T)=-\frac{\partial}{\partial H}(\frac{F}{k_BT}) The Attempt at a Solution For me it looks that magnetisation is zero. By just doing the...

I'm trying to simulate a 100x100 Ising model in matlab. So far I've tried the metropolis method (which seems to work), but I'm having problems with the heat bath method. I'm not sure how it's supposed to work (I can't get the spins to all take the same +1 or -1 value even at really low...

Ising Model Monte Carlo -- interpretations Hi, I am trying to solve and understand the classical Ising Model through a classical Monte Carlo simulation. I notice that if I begin with a ferromagnetic initial state, then the magnetization is more or less constant for a wide range of temperatures...

Hi, So I'm trying to solve the 2D Ising Model using a simple Monte Carlo algorithm, for small square lattices, imposing periodic boundary conditions. Before I compute any thermodynamic quantities though, I want to study the energetics of the system with only nearest-neighbour interactions...

The title says it all. It looks like the configuration probability only depends on where you want to go, not what state you are in now. Yet when I watch simulations, there is clearly a dependence on the previous state. Is there something pretty basic I'm misunderstanding about configuration...

Hi, I'm currently using the Monte Carlo Metropolis algorithm to investigate the 2D Ising model. I have an NxN lattice of points with periodic boundary conditions imposed. I was wondering if anyone could explain why the sharpness of the phase transition is affected by the size of N? I.e...

I'm doing a computational physics project where I'm looking at the Ising model in 2D and external magnetics field. I start with all the spins in same directions my grid is 30x30 and I use periodic boundry conditions. I start with all the spins in the same direction (+1). I do about 150000...

Hi I'm working on a MATLAB simulation of the 2D Ising model, and would like to verify my code and its results. One thing I'd like to try and observe is the transition from anti-ferromagnet to ferromagnet, but I'm not sure how to create the initial lattice in Matlab. I've already made a...

Hello,I am doing a research related to Ising Model in m research, evolution of a multi-qubit Ising system with the initial and final Hamiltonian is given by: (1) Hi=(-1/2)\sum\sigma^{(i)}_{x} (2) Hf=(-1/2)\sumhi\sigma^{(i)}_{z}+(1/2)\sumJ_{ij}\sigma^{(i)}_{z}\sigma^{(j)}_{z} (3)...

Hi all, I am doing a program to simulate the 2D Ising Model under the metropolis algorithm. In order to check my results I would like to compare them with the analytical expressions for the mean energy, magnetization, specific heat and magnetic susceptibility. I already found the...

Hi all, I am doing a program to simulate the 2D Ising Model under the metropolis algorithm. In order to check my results I would like to compare them with the analytical expressions for the mean energy, magnetization, specific heat and magnetic susceptibility. I already found the...

the hamiltonian is H=-J \sum_{l=1}^N \sigma_l^z \sigma_{l+1}^z+ g \sigma_l^x here we assume periodic boundary condition my problem is, what is the highest possible degeneracy of the levels? initially i expected 2 but numerically i find that it is 4 i cannot understand it

Hi guys, I'm working through past papers and I have a problem with deriving the renormalised scaling of the following: [PLAIN]http://dl.dropbox.com/u/16658950/helpme.JPG I'm doing the rescaling as I would for a 1D ising model decimated with l = 2 (so every other spin, but N=4 in this...

Hi I'm looking for some help with trying to understand how to use the metropolis algorithm for the 2D ising model. In the problem i am trying to solve, the Hamiltonian is simply H= - sum(Si). I am given a probability function= exp[-H/T] / Z(T) where Z is the partition function which i found...

Hello, First of all, sorry if my question is trivial but I'm not a physicist ;-) I heard a lot about the Ising model used to compute the energy of a system with 2 states. This model seems to be a bit "simple" because it assumes that particles interact with their nearest neighbors only. I was...

I'm stuck on a question about deriving an expression for the magnetic susceptibility in terms of the variance of the magnetisation for a simple 2d square ising model. I get the derivation of the specific heat, and I know am supposed to do something similar to get to the expression for...

Hello, actually, I am not a physicist, I am a Computer Science Graduate Student, Anyways, I am doing a research related to Ising Model My question is about the energy in Ising Model the following statement is written in "History of the Lenz-Ising Model" paper: "when two neighboring spins...

Hi, I have the problema of implementing wolff's algorithm for ising model in 2-D lattice. Has anyone ever done this algorithm in FORTRAN ? I have questions of how to join the clusters. Alexandre

Homework Statement I'm trying to program the 2D Ising model with Java, but for some reason, I cannot get magnetization to come out right. The energy and magnetization appear to be acting right for increase and decrease in temperatures, but I don't see anything significant at a critical...

I am curious to know the Ising model can be applied to high temperature superconducting materials. If so are there any papers significant papers on this subject that I should know about. Thanks to anyone in advance who can answer this question.

hellow everybody i have a problem in styding the critical bihaviour of the tow dimensional ising model when i use periodiques boundary conditions i found that the fixed point for this case is the PRG equation that mean the following recursion relation...

Hi i want to calculate average number of spins at site i for ising model <ni> i want do this by transfer matrix,how can i do this?

Hi, I'm slightly confused about how to prove that: \chi=\vartheta<M>/\varthetaH is equal to... \chi=(<M2>-<M>2 )/ T I've expressed <M> as \sumMsexp(-E/kBT) / \sumexp(-E/kBT) and know that E=-J\sumSiSj-H\sumSi But seem to get lost in the...

I am learning the 1D ising model (spin 1/2), without external field and considering the nearest site interaction, the hamiltonian for 1D chain is simple H = -J\sum_i S_iS_{i+1} Since each spin can only take either +1 or -1, we can write the transition matrix as T = \left(...

When I studied renormalisation for the Ising model the procedure was to sum over every second spin and then find a new coupling which produced the same physics. This leads to a relation between the coupling at different scales of the form K(2s)=f(K(s)) Where K is the coupling, s is the...

Homework Statement Can someone please explain to me why there can never be a phase transition in the 1D Ising model? Homework Equations The Attempt at a Solution I have read the argument that if we start at T=0, all spins along the 1D chain are aligned (say up). Then if we...

The Ising model starts with an assumption that the nearby spins reach lower potential by pointing at the same direction. However, two magnets would reach lower potential by pointing at different directions. What is the mechanism, that in the first place makes spins attempt to align themselves in...

I was trying to understand why for every spin configuration of a ferromagnetic system, there exists a corresponding isoenergetic state of an antiferromagnetic system. Can I treat an antiferromagnetically coupled 1-D ising model as a combination of two interpenetrating sublattices which are...

I'm having trouble understanding how changing parameters in the ising model leads to first order phase transitions. I understand how the intersection of \frac{kT}{2nJS} (\eta - \frac{g \mu_o H_o}{kT} ) = B_s(\eta) where B_s(\eta) is the Brouillion func leads (in the absence of a field H) to...

Hi, I'm looking for something (books or other), about Ising Model. Can anyone of you help me? Thank you

Homework Statement Consider a 2 dimensional three state Ising model with ferromagnetic coupling J, where si = −1, 0, 1 in a magnetic field h on a triangular lattice. Construct a mean field equation for the magnetization m. The Attempt at a Solution I don't know how to start. 2d ising...

I've read in an article that the 1D Ising Model in a random field is a frustrated system. But what does it mean for the 1D RFIM to be frustrated? The internet is very unhelpful. I'd appreciate it if someone could answer this for me. Thanks.