相关论文: Low temperature behavior of finite-size one-dimens…
We study the critical Ising model with free boundary conditions on finite domains in $\mathbb{Z}^d$ with $d\geq4$. Under the assumption, so far only proved completely for high $d$, that the critical infinite volume two-point function is of…
We rewrite the exact expression for the finite temperature two-point correlation function for the magnetization as a partition function of some field theory. This removes singularities and provides a convenient form to develop a virial…
We consider the planar Ising model in a finite square box and we replace the temperature parameter with a function depending on the magnetization. This creates a feedback from the spin configuration onto the parameter, which drives the…
We present a method for evaluating the partition function in a varying external field. Specifically, we look at the case of a non-interacting, charged, massive scalar field at finite temperature with an associated chemical potential in the…
In the high dimension (mean field) limit the susceptibility and the second moment correlation length of the Ising ferromagnet depend on temperature as chi(T)=tau^{-1} and xi(T)=T^{-1/2}tau^{-1/2} exactly over the entire temperature range…
We derive an exact path integral formulation for the partition function for the Ising model using a mapping between spins and poles of a Laurent expansion for a field on the complex plane. The advantage in using this formulation for the…
Qualitative and quantitative information about critical phenomena is provided by the distribution of zeros of the partition function in the complex plane. We apply this idea to Ising models on non-periodic systems based on substitution. In…
The complete form of the high-temperature expansion of the one-loop contribution to the free energy of a scalar field on a stationary gravitational background is derived. The explicit expressions for the divergent and finite parts of the…
We study the second-moment correlation length and the reduced susceptibility of two ferromagnetic Ising models with zero-temperature ordering. By introducing a scaling variable motivated by high-temperature series expansions, we are able to…
In extensive Monte Carlo simulations the phase transition of the random field Ising model in three dimensions is investigated. The values of the critical exponents are determined via finite size scaling. For a Gaussian distribution of the…
The Ising model in two dimensions with special toroidal boundary conditions is analyzed. These boundary condition, which we call duality twisted boundary conditions, may be interpreted as inserting a specific defect line ("seam") in the…
The two-component mixture of Bose particles with short-range pairwise interaction at finite temperatures in three dimensions is considered. Particularly we examine, by means of the large-$N$ expansion technique, the stability of mixed state…
Finite-size scaling, finite-size corrections, and boundary effects for critical systems have attracted much attention in recent years. Here we derive exact finite-size corrections for the free energy F and the specific heat C of the…
We investigate scaling phenomena at first-order quantum transitions, when the boundary conditions favor one of the two phases. We show that the corresponding finite-size scaling behavior, arising from the interplay between the driving…
The Ising model describes collective behaviors such as phase transitions and critical phenomena in various physical, biological, economical, and social systems. It is well-known that spontaneous phase transition at finite temperature does…
The study of zeros of partition functions, initiated by Yang and Lee, provides an important qualitative and quantitative tool in the study of critical phenomena. This has frequently been used for periodic as well as hierarchical lattices.…
We investigate the laws of coarsening of a two-dimensional system of Ising spins evolving under single-spin-flip irreversible dynamics at low temperature from a disordered initial condition. The irreversibility of the dynamics comes from…
We study some properties of the Ising model in the plane of the complex (energy/temperature)-dependent variable $u=e^{-4K}$, where $K=J/(k_BT)$, for nonzero external magnetic field, $H$. Exact results are given for the phase diagram in the…
In this paper, we theoretically study the critical properties of the classical spin-1 Ising model using two approaches: 1) the analytical low-temperature series expansion and 2) the numerical Metropolis Monte Carlo technique. Within this…
High-temperature expansions are presently the only viable approach to the numerical calculation of the higher susceptibilities for the spin and the scalar-field models on high-dimensional lattices. The critical amplitudes of these…