Related papers: Correlation functions in the two-dimensional rando…
We develop a transfer matrix method to compute exactly the spin-spin correlation functions of Bethe lattice spin models in the external magnetic field h and for any temperature T. We first compute the correlation function for the most…
One-dimensional systems with short-range interactions cannot exhibit a long-range order at nonzero temperature. However, there are some particular one-dimensional models, such as the Ising-Heisenberg spin models with a variety of lattice…
The properties of the pure-site clusters of spin models, i.e. the clusters which are obtained by joining nearest-neighbour spins of the same sign, are here investigated. In the Ising model in two dimensions it is known that such clusters…
Using the results of large scale numerical simulations we study the probability distribution of the pseudo critical temperature for the three-dimensional Edwards-Anderson Ising spin glass and for the fully connected Sherrington-Kirkpatrick…
We investigate spin-spin correlation functions in the low temperature phase of spin-glasses. Using the replica field theory formalism, we examine in detail their infrared (long distance) behavior. In particular we identify a longitudinal…
Averaged spin-spin correlation function squared $\overline{<\sigma(0)\sigma(R)>^{2}}$ is calculated for the ferromagnetic random bond Potts model. The technique being used is the renormalization group plus conformal field theory. The…
A general technique of exact calculation of any correlation functions for the special class of one-dimensional spin models containing small clusters of quantum spins assembled to a chain by alternating with the single Ising spins is…
The correlation length plays a pivotal role in finite-size scaling and hyperscaling at continuous phase transitions. Below the upper critical dimension, where the correlation length is proportional to the system length, both finite-size…
We show by numerical simulations that the correlation function of the random field Ising model (RFIM) in the critical region in three dimensions has very strong fluctuations and that in a finite volume the correlation length is not…
Using extensive Monte Carlo simulations we study aging properties of two disordered systems quenched below their critical point, namely the two-dimensional random-bond Ising model and the three-dimensional Edwards-Anderson Ising spin glass…
In this article, we have employed Monte Carlo simulations to study the Ising model on a two-dimensional additive small-world network (A-SWN). The system model consists of a LxL square lattice where each site of the lattice is occupied for a…
We develop a recently-proposed mapping of the two-dimensional Ising model with random exchange (RBIM), via the transfer matrix, to a network model for a disordered system of non-interacting fermions. The RBIM transforms in this way to a…
We show that the functional renormalization group (FRG) allows for the calculation of the probability distribution function of the sum of strongly correlated random variables. On the example of the three-dimensional Ising model at…
We study the correlation length of the two-dimensional Ising spin glass with a Gaussian distribution of interactions, using an efficient Monte Carlo algorithm proposed by Houdayer, that allows larger sizes and lower temperatures to be…
A previously introduced real space renormalization-group treatment of the random transverse-field Ising spin chain is extended to provide detailed information on the distribution of the energy gap and the end-to-end correlation function for…
The effects of random magnetic fields are considered in an Ising spin-glass model defined in the limit of infinite-range interactions. The probability distribution for the random magnetic fields is a double Gaussian, which consists of two…
Geometric representations provide a useful perspective on critical phenomena in the Ising model. In a recent study [Phys. Rev. E 112, 034118 (2025)], we found that the two-dimensional critical Ising model exhibits two consecutive…
We find the cross-over behavior for the spin-spin correlation function for the 2D Ising and 3-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation approach of the perturbation series…
In this work we propose a new numerical method to evaluate the critical point, the susceptibility critical exponent and the correlation length critical exponent of the three dimensional Ising model without external field using an algorithm…
The critical behavior of the random transverse-field Ising model in finite dimensional lattices is governed by infinite disorder fixed points, several properties of which have already been calculated by the use of the strong disorder…