Related papers: The Phase Transition in Statistical Models Defined…
The linear fractional stable motion generalizes two prominent classes of stochastic processes, namely stable L\'evy processes, and fractional Brownian motion. For this reason it may be regarded as a basic building block for continuous time…
We use a simplified model which is based on the same physics as inherent in most statistical models for nuclear multifragmentation. The simplified model allows exact calculations for thermodynamic properties of systems of large number of…
We study the long-time, large scale transport in a three-parameter family of isotropic, incompressible velocity fields with power-law spectra. Scaling law for transport is characterized by the scaling exponent $q$ and the Hurst exponent…
A first order phase transition is found in a model which was introduced originally by Murthy and Shankar [Phys. Rev. B 60, 6517 (1999)] to describe systems of generalised exclusion statistics. I characterise the phase transition in the…
The temperature phase transition in the $N$-component scalar field theory with spontaneous symmetry breaking is investigated using the method combining the second Legendre transform and with the consideration of gap equations in the extrema…
We employ the microcanonical inflection-point analysis method, developed for the systematic identification and classification of phase transitions in systems of any size, to study the two-dimensional Ising model at various lattice sizes and…
Statistical systems on random networks can be formulated in terms of partition functions expressed with integrals by regarding Feynman diagrams as random networks. We consider the cases of random networks with bounded but generic degrees of…
The collective amplitude mode of the order parameter in displacive ferroelectrics, termed the ferron, represents the amplitude fluctuations of long-range ordered polarization. At temperatures well below phase transition temperature $T_c$,…
In this work we employ a simple pairing interaction model in order to study and classify an eventual pairing phase transition in finite fermionic systems. We show that systems with as few as 10-16 fermions can exhibit clear features…
We have introduced a novel Majorana representation of S=1/2 spins using the Jordan-Wigner transformation and have shown that a generalized spin model of Kitaev defined on a brick-wall lattice is equivalent to a model of non-interacting…
We derive rates of convergence for limit theorems that reveal the intricate structure of the phase transitions in a mean-field version of the Blume-Emery-Griffith model. The theorems consist of scaling limits for the total spin. The model…
Random matrix models provide a phenomenological description of a vast variety of physical phenomena. Prominent examples include the eigenvalue statistics of quantum (chaotic) systems, which are conveniently characterized using the spectral…
Two known distinct examples of one-dimensional systems which are known to exhibit a phase transition are critically examined: (A) a lattice model with harmonic nearest-neighbor elastic interactions and an on-site Morse potential, and (B)…
We consider a slight modification of the frog model. For a given graph, each vertex has $\mathrm{Poisson}(\lambda)$ particles (or frogs). At time zero, only the particles at the origin are active, and all the other particles are sleeping.…
Distinguished from the system with one order parameter, systems described by two or more order parameters will manifest more complex and much richer phase diagram and critical phenomena. In systems of two order parameters, the phase…
We investigate the collective dynamics of nonlinearly interacting modes in multimode photonic settings with long-range couplings. To this end, we have established a connection with the theory of spin networks. The emerging "photonic spins"…
We study numerically the paramagnetic phase of the spin-1/2 random transverse-field Ising chain, using a mapping to non-interacting fermions. We extend our earlier work, Phys. Rev. 53, 8486 (1996), to finite temperatures and to dynamical…
We survey known results about phase transitions in various models of statistical physics when the underlying space is a nonamenable graph. Most attention is devoted to transitive graphs and trees.
Using the numerical approach for a study of the thermodynamic properties of the nonuniform one-dimensional spin-1/2 isotropic XY model in a transverse field we examine different lattice distortions to reveal which spin-Peierls phases are…
Area fluctuations of a Brownian excursion are described by the Airy distribution, which found applications in different areas of physics, mathematics and computer science. Here we generalize this distribution to describe the area…