A typical problem with Monte Carlo simulations in statistical physics is that they do not allow for a direct calculation of the free energy. For systems at criticality, this means that one cannot calculate the central charge in a Monte Carlo simulation. We present a novel finite size scaling technique for two-dimensional systems on a geometry of L×M , and focus on the scaling behavior in M/L. We show that the finite size scaling behavior of the stress tensor, the operator that governs the anisotropy of the system, allows for a determination of the central charge and critical exponents. The expectation value of the stress tensor can be calculated using Monte Carlo simulations. Unexpectedly, it turns out that the stress tensor is remarkably insensitive for critical slowing down, rendering it an easy quantity to simulate. We test the method for the Ising model (with central charge c = 1 2 ), the Ashkin-Teller model (c = 1), and the F-model (also c = 1).

We argue that colossal magnetoresistance is a critical phenomenon and propose a mechanism to describe it. The mechanism relies on the halfmetallic behavior of the materials showing colossal magnetoresistance, and yields a correlated percolation model that, we argue, captures all qualitative features of colossal magnetoresistance, above as well as below the Curie temperature. The model only serves for revealing the underlying mechanism of colossal magnetoresistance, and does not aim to reproduce precise, numerical results. 72.15.Gd, 64.60.Cn, 73.50.Jt *

We study the phase diagram of the body-centered solid on solid ͑BCSOS͒ model with an extended interaction range using transfer matrix techniques, pertaining to the ͑100͒ surface of single-component fcc and bcc crystals. The model shows a 2ϫ2 reconstructed phase and a disordered flat phase. The deconstruction transition between these phases merges with a Kosterlitz-Thouless line, showing an interplay of Ising and Gaussian degrees of freedom. As in studies of the fully frustrated XY model, exponents deviating from Ising are found. We conjecture that tricritical Ising behavior may be a possible explanation for the non-Ising exponents found in those models.

We present some exact results on percolation properties of the Ising model, when the range of the percolating bonds is larger than nearest-neighbors. We show that for a percolation range to next-nearest neighbors the percolation threshold T p is still equal to the Ising critical temperature T c , and present the phase diagram for this type of percolation. In addition, we present Monte Carlo calculations of the finite size behavior of the correlated resistor network defined on the Ising model. The thermal exponent t of the conductivity that follows from it is found to be t = 0.2000 ± 0.0007. We observe no corrections to scaling in its finite size behavior.PACS numbers: 64.60. Ak, 64.60.Fr, 05.50.+q Typeset using REVT E X The connection between percolation and the Ising model has been a popular subject for a long time. One considers so-called Ising clusters made up of nearest-neighbor spins with the same spin value. The connectivity behavior of these clusters is called correlated site percolation, as the probability distribution of the percolating and non-percolating sites is a correlated one.The interest in this problem arose because these Ising clusters were believed to have the same properties as the droplets in the droplet model [1], i.e. they should diverge at the Ising critical point with the same critical exponents as those of the Ising model. It became clear that they did indeed diverge [2] at the Ising critical point, but not [3] with Ising exponents. An alternative cluster definition was needed to have clusters with the properties of droplets in the droplet model. These clusters, called Coniglio-Klein clusters [4], are defined by putting bonds between each pair of nearest neighbor up-spins, but now with a probability p = 1 − exp(−2K), where K is the Ising coupling. Not all bonds of the Ising clusters appear in the Coniglio-Klein clusters, such that the latter are, in that sense, 'smaller' than Ising clusters. The Coniglio-Klein clusters display [4] the right critical behavior: their diverge at the Ising critical point, their linear size diverges as the Ising correlation length, and the mean cluster size behaves as the susceptibility.Both the Ising clusters and the Coniglio-Klein clusters have their percolation point at the Ising critical temperature, albeit with different critical behavior. The full picture of this cluster behavior emerged [5,6] when the behavior of both types of clusters was identified with the phase diagram of the q-state dilute Potts model in the limit q → 1. The tricritical point in this phase diagram describes the behavior of the Ising clusters. This tricritical point falls in the same universality class as the Ising critical point [7] in the sense that the central charge is c = 1/2, but the critical exponents involved in the behavior of the Ising clusters do not fit into the ; they correspond to half-integer values of the unitary grid. The Coniglio-Klein clusters are described by the 1 + 1 state symmetric fixed point in this phase diagram.Our motivation to reconsider the problem ...

Monte Carlo or Molecular Dynamics calculations of surfaces of Lennard-Jones systems often indicate, apart from a gradual disordering of the surface called surface melting, the presence of a phase transition at the surface, but cannot determine the nature of the transition. In the present paper, we provide for a link between the continuous Lennard-Jones system and a lattice model. We apply the method for the (001) surface of a Lennard-Jones fcc structure pertaining to Argon. The corresponding lattice model is a Body Centered Solid on Solid model with an extended range of interaction, showing in principle rough, flat and disordered flat phases. We observe that entropy effects considerably lower the strength of the effective couplings between the atoms. The Argon (001) face is shown to exhibit a phase transition at T=70.5 +- 0.5 K, and we identify this transition as roughening. The roughening temperature is in good correspondence with experimental results for Argon.Comment: 17 pages REVTeX, 14 uuencoded postscript figures appende