Related papers: On phase transition in the hard-core model on ${\b…
Phase transitions are investigated in the Bose-Fermi-Hubbard model in the mean field and hard-core boson approximations for the case of infinitely small fermion transfer and repulsive on-site boson-fermion interaction. The behavior of the…
We use high order linked cluster series to investigate the hard core boson model on the triangular lattice, at zero temperature. Our expansions, in powers of the hopping parameter $t$, probe the spatially ordered `solid' phase and the…
We study the zero temperature phase diagram of hard core bosons in two dimensions subjected to three types of background potentials: staggered, uniform, and random. In all three cases there is a quantum phase transition from a superfluid…
The finite-temperature phase diagram of the Hubbard model in $d=3$ is obtained from renormalization-group analysis. It exhibits, around half filling, an antiferromagnetic phase and, between 30%--40% electron or hole doping from half…
Hard-core bosons on a triangular lattice with nearest neighbor repulsion are a prototypical example of a system with supersolid behavior on a lattice. We show that in this model the physical origin of the supersolid phase can be understood…
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.…
The temperature induced phase transition is investigated in the one-component scalar field \phi^4 model on the lattice. Using the GPU cluster a huge amount of Monte Carlo simulation data is collected for a wide interval of coupling values.…
We show that a certain model for the spread of an infection has a phase transition in the recuperation rate. The model is as follows: There are particles or individuals of type A and type B, interpreted as healthy and infected,…
We investigate the asymptotic behavior as $\varepsilon \to 0$ of singularly perturbed phase transition models of order $n \geq 2$, given by \begin{align} G_\varepsilon^{\lambda,n}[u] := \int_I \frac 1\varepsilon W(u)…
In this thesis, we present results on phase transition for two models: the semi-infinite Ising model with a decaying field, and the long-range Ising model with a random field. We study the semi-infinite Ising model with an external field…
We determine the zero-temperature phase diagram of the hard-core Bose-Hubbard model on a square lattice by mean-field theory supplemented by a linear spin-wave analysis. Due to the interplay between nearest and next-nearest neighbor…
We study the semi-infinite Ising model with an external field $h_i = \lambda |i_d|^{-\delta}$, $\lambda$ is the wall influence, and $\delta>0$. This external field decays as it gets further away from the wall. We are able to show that when…
Given a field $\{B(x)\}_{x\in\mathbf{Z}^d}$ of independent standard Brownian motions, indexed by $\mathbf{Z}^d$, the generator of a suitable Markov process on $\mathbf{Z}^d,\,\,\mathcal{G},$ and sufficiently nice function…
We study the low temperature properties of the two-dimensional weakly interacting Hubbard model on $\ZZZ^2$ with renormalized chemical potential $\mu=2-\mu_0$, $\mu_0=10^{-10}$ fixed, in which case the Fermi surface is close to a perfect…
Binary mixtures of lamellar colloids represented by hard platelets are studied within a generalization of the Zwanzig model for rods, whereby the square cuboids can take only three orientations along the $x$, $y$ or $z$ axes. The free…
We study the triangular lattice bilayer Heisenberg model with antiferromagnetic interplane coupling $J_\perp$ and nearest neighbour intraplane coupling $J= \lambda J_\perp$, which can be ferro- or antiferromagnetic, by expansions in…
For the hard-core lattice gas model defined on independent sets weighted by an activity $\lambda$, we study the critical activity $\lambda_c(\mathbb{Z}^2)$ for the uniqueness/non-uniqueness threshold on the 2-dimensional integer lattice…
The phase transitions at finite temperatures in the systems described by the Bose-Fermi-Hubbard model are investigated in this work in the framework of the selfconsistent random phase approximation. The case of the hard-core bosons is…
We consider the hard-core lattice gas model on Z^d and investigate its phase structure in high dimensions. We prove that when the intensity parameter exceeds Cd^{-1/3}(log d)^2, the model exhibits multiple hard-core measures, thus improving…
The topological theory of phase transitions has its strong point in two theorems proving that, for a wide class of physical systems, phase transitions necessarily stem from topological changes of some submanifolds of configuration space. It…