Related papers: Phase transitions in Delaunay Potts models
We identify ground states of one-dimensional fermionic systems subject to competing repulsive interactions of finite range, and provide phenomenological and fundamental signatures of these phases and their transitions. Commensurable…
The competition between interactions and dissipative processes in a quantum many-body system can drive phase transitions of different order. Exploiting a combination of cluster methods and quantum trajectories, we show how the systematic…
This article contains our comments and views on the status of the current understanding of phase transitions in systems with only hard-core interactions, based on our work in this area. The equation of state for the hard sphere gas in…
We study the system of multi-body interacting bosons on a two dimensional optical lattice and analyze the formation of bound bosonic pairs in the context of the Bose-Hubbard model. Assuming a repulsive two-body interaction we obtain the…
We describe a phase transition in continuum limits of interacting particle systems that exhibits a vertical bifurcation diagram. The transition is mediated by a competition short-range repulsion and long-range attraction. As a consequence…
The one-dimensional extended isotropic XY model (s=1/2) in a transverse field with uniform long-range interactions among the \textit{z} components of the spin is considered. The model is exactly solved by introducing the gaussian and…
Isotropic pair potentials that are bounded at the origin have been proposed from time to time as models of the effective interaction between macromolecules of interest in the chemical physics of soft matter. We present a thorough study of…
The superradiant phase transition in the dissipative Dicke lattice model, driven by on-site collective atom-photon interactions and inter-site photon hopping, is a cornerstone of nonequilibrium quantum many-body physics. However, little is…
It has been proposed (Phys. Rev. E {\bf 71}, 026121 (2005)) that unlike the short range contact process, a long-range counterpart may lead to the existence a discontinuous phase transition in one dimension. Aiming at exploring such link,…
The aim of this paper is to study a PDE model for two diffusing species interacting by local size exclusion and global attraction. This leads to a nonlinear degenerate cross-diffusion system, for which we provide a global existence result.…
We study the joint asymptotic behavior of spacings between particles at the edge of multilevel Dyson Brownian motions, when the number of levels tends to infinity. Despite the global interactions between particles in multilevel Dyson…
We study the phase behaviour of a fluid composed of particles which interact via a pair potential that is repulsive for large inter-particle distances, is attractive at intermediate distances and is strongly repulsive at short distances…
In multitype lattice gas models with hard-core interaction of Widom--Rowlinson type, there is a competition between the entropy due to the large number of types, and the positional energy and geometry resulting from the exclusion rule and…
We investigate the phase diagram of a one-dimensional model of hardcore bosons or spinless fermions with tunable nearest-neighbor interactions. By introducing alternating repulsive and attractive interactions on consecutive bonds, we show…
We study the decay of two repulsively interacting bosons tunneling through a delta potential barrier by direct numerical solution of the time-dependent Schr\"odinger equation. The solutions are analyzed according to the regions of particle…
We consider the $Q$-state Potts model on $\mathbb Z^d$, $Q\ge 3$, $d\ge 2$, with Kac ferromagnetic interactions and scaling parameter $\ga$. We prove the existence of a first order phase transition for large but finite potential ranges.…
In this paper we study a continuum version of the Potts model. Particles are points in R^d, with a spin which may take S possible values, S being at least 3. Particles with different spins repel each other via a Kac pair potential. In mean…
We consider a $d$-dimensional gas in canonical equilibrium under pairwise screened Coulomb repulsion and external confinement, and subject to a volume constraint. We show that its excess free energy displays a generic third-order…
We analyze the combined effect of the long range Coulomb (LRC) interaction and of surface energy on first order density-driven phase transitions in the presence of a compensating rigid background. We study mixed states formed by regions of…
The aim of this paper is to discuss the mathematical modeling of Brownian active particle systems, a recently popular paradigmatic system for self-propelled particles. We present four microscopic models with different types of repulsive…