相关论文: Random-energy model in random fields
We explore ensemble inequivalence in long-range interacting systems by studying an XY model of classical spins with ferromagnetic and nematic coupling. We demonstrate the inequivalence by mapping the microcanonical phase diagram onto the…
We examine the spatial distribution of electrons generated by a fixed energy point source in uniform, parallel electric and magnetic fields. This problem is simple enough to permit analytic quantum and semiclassical solution, and it harbors…
We introduce the boson and the fermion point processes from the elementary quantum mechanical point of view. That is, we consider quantum statistical mechanics of canonical ensemble for a fixed number of particles which obey Bose-Einstein,…
A unified treatment for the existence of free energy in several random energy models is presented. If the sequence of distributions associated with the particle systems obeys a large deviation principle, then the free energy exists almost…
The microcanonical ensemble is in important physical situations different from the canonical one even in the thermodynamic limit. In contrast to the canonical ensemble it does not suppress spatially inhomogeneous configurations like phase…
Here we present two explicit counterexamples to the widely spread beliefs about an exclusive role of bimodality as the first order phase transition signal. On the basis of an exactly solvable statistical model generalizing the statistical…
The phase diagram of the simplest approximation to Double-Exchange systems, the bosonic Double-Exchange model with antiferromagnetic super-exchange coupling, is fully worked out by means of Monte Carlo simulations, large-N expansions and…
We compare phase transition(-like) phenomena in small model systems for both microcanonical and canonical ensembles. The model systems correspond to a few classical (non-quantum) point particles confined in a one-dimensional box and…
We study the quantum phase transition in the three-dimensional disordered itinerant antiferromagnet by Monte-Carlo simulations of the order-parameter field theory. We find strong evidence for the transition being controlled by an…
In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature/energy range around the critical point. By combining the replica-exchange algorithm with cluster updates…
We introduce a spin-1 version of the random energy model with crystal field. Crystal field controls the density of 0 spins in the system. We solve the model in the micro-canonincal ensemble. The model has a spin-glass transition at a finite…
The grand canonical ensemble lies at the core of quantum and classical statistical mechanics. A small system thermalizes to this ensemble while exchanging heat and particles with a bath. A quantum system may exchange quantities represented…
The thermodynamic properties of bosons moving in a harmonic trap in an arbitrary number of dimensions are investigated in the grand canonical, canonical and microcanonical ensembles by applying combinatorial techniques developed earlier in…
Ensemble inequivalence has been previously displayed only for long-range interacting systems with non-extensive energy. In order to perform the thermodynamic limit, such systems require an unphysical, so-called, Kac rescaling of the…
The scaling theory of critical phenomena has been successfully extended for classical first order transitions even though the correlation length does not diverge in these transitions. In this paper we apply the scaling ideas to quantum…
A high-order extension is presented for the electromagnetic gyrokinetic formulation in which the parallel canonical momentum is taken as one of phase space coordinates. The high-order displacement vector associated with the guiding-center…
We present a method using Feynman-like diagrams to calculate the statistical properties of random many-body potentials. This method provides a promising alternative to existing techniques typically applied to this class of problems, such as…
Based on numerical simulation and local stability analysis we describe the structure of the phase space of the edge/triangle model of random graphs. We support simulation evidence with mathematical proof of continuity and discontinuity for…
We present for the first time to the nuclear physics community the Hamiltonian Mean Field (HMF) model. The model can be solved analytically in the canonical ensemble and shows a second-order phase transition in the thermodynamic limit.…
We study percolation and the random cluster model on the triangular lattice with 3-body interactions. Starting with percolation, we generalize the star--triangle transformation: We introduce a new parameter (the 3-body term) and identify…