Tagged Questions
2
votes
1answer
63 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
votes
0answers
31 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
80 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 ?
2
votes
3answers
271 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
votes
0answers
54 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?
1
vote
1answer
105 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
votes
0answers
59 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
54 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
1answer
78 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}
...
4
votes
1answer
154 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 ...
0
votes
4answers
121 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
votes
1answer
296 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 ...
4
votes
1answer
232 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 ...
7
votes
0answers
98 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
votes
1answer
103 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 ...
3
votes
1answer
168 views
Scaling with the Ising Model
I am stuck with one formula in the CFT book by Di Francesco and al. Chapter 3. Equation 3.46 third step, for those who don't have the book, he integrates out degrees of freedom from the Ising Model by ...
3
votes
1answer
69 views
Random bond Ising model and computational efficiency
If you want to find the ground state of the 2d random bond Ising model (no field), a computationally efficient algorithm exists to do it for you (based on minimum weight perfect matching). What about ...
7
votes
0answers
164 views
Information geometry of 1D Ising model in complex magnetic field regime
Consider the one-dimensional Ising model with constant magnetic field and node-dependent interaction on a finite lattice, given by
$$H(\sigma) = -\sum_{i = 1}^N J_i\sigma_i\sigma_{i + 1} - h\sum_{i = ...
6
votes
1answer
258 views
What is the information geometry of 1D Ising model for a complex magnetic field?
Consider the one-dimensional Ising model with constant magnetic field and node-dependent interaction on a finite lattice, given by
$$H(\sigma) = -\sum_{i = 1}^N J_i\sigma_i\sigma_{i + 1} - h\sum_{i = ...
13
votes
1answer
72 views
Phase Transition in the Ising Model with Non-Uniform Magnetic Field
Consider the Ferromagnetic Ising Model ($J>0$) on the lattice $\mathbb{Z}^2$ with the Hamiltonian with boundary condition $\omega\in\{-1,1\}$ formally given by
$$
...
2
votes
2answers
291 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 ...
6
votes
2answers
680 views
Efficiency of Metropolis algorithm
Context is 1D Ising model. Metropolis algorithm is used for simulate that model. Among all possible spins configurations (states) that algorithm generates only states with the desired Boltzmann ...
7
votes
3answers
254 views
Estimating Partition functions
I have a finite state ensemble with an energy functional (you can think of it as an ferromagnetic Ising model if you like), and I need very careful estimates of the partition function. What methods ...
7
votes
3answers
793 views
Zero magnetization of spin model without external magnetic field
For a given Hamiltonian with spin interaction, say Ising model
$$H=-J\sum_{i,j} s_i s_j$$
in which there are no external magnetic field. The Hamiltonian is invariant under transformation $s_i ...
10
votes
2answers
945 views
Ising model for dummies
I am looking for some literature on the Ising model, but I'm having a hard time doing so. All the documentation I seem to find is way over my knowledge.
Can you direct me to some documentation on it ...
9
votes
4answers
784 views
How many Onsager's solutions are there?
Update: I provided an answer of my own (reflecting the things I discovered since I asked the question). But there is still lot to be added. I'd love to hear about other people's opinions on the ...
