Related papers: Phase coexistence of gradient Gibbs states
We define a finite Borel measure of Gibbs type, supported by the Sobolev spaces of negative indexes on the circle. The measure can be seen as a limit of finite dimensional measures. These finite dimensional measures are invariant by the…
Phase diagrams are essential tools of the materials scientist, showing which phases are at equilibrium under a set of applied thermodynamic conditions. Essentially all phase diagrams today are two dimensional, typically constructed with…
We consider irreversible translation-invariant interacting particle systems on the $d$-dimensional cubic lattice with finite local state space, which admit at least one Gibbs measure as a time-stationary measure. Under some mild degeneracy…
We prove that nonlinear Gibbs measures can be obtained from the corresponding many-body, grand-canonical, quantum Gibbs states, in a mean-field limit where the temperature T diverges and the interaction behaves as 1/T. We proceed by…
We study a model of spatial random permutations over a discrete set of points. Formally, a permutation $\sigma$ is sampled proportionally to the weight $\exp\{-\alpha \sum_x V(\sigma(x)-x)\},$ where $\alpha>0$ is the temperature and $V$ is…
In this paper we study homogeneous Gibbs measures on a Cayley tree, subjected to an infinite-temperature Glauber evolution, and consider their (non-)Gibbsian properties. We show that the intermediate Gibbs state (which in zero field is the…
In this note, we study the hyperbolic stochastic damped sine-Gordon equation (SdSG), with a parameter $\beta^2 > 0$, and its associated Gibbs dynamics on the two-dimensional torus. After introducing a suitable renormalization, we first…
During his time at Royal Institute of Technology (Kungliga Tekniska Hogskolan, KTH) in Sweden, the present author learned nonequilibrium thermodynamics from Mats Hillert. The key concepts are the separation of internal and external…
Disorder in quantum many-body systems can drive transitions between ergodic and non-ergodic phases, yet the nature--and even the existence--of these transitions remains intensely debated. Using a two-dimensional array of superconducting…
We derive the classical Gibbs measure on $\mathbb{T}^2$ associated with the fractional Bessel interaction potential $\widehat{v}_\beta(k)=\langle k\rangle^{-\beta}$ from a renormalized grand-canonical quantum Bose gas with the same…
The phase transitions in the transverse field Ising model in a competing spatially modulated (periodic and oscillatory) longitudinal field are studied numerically. There is a multiphase point in absence of the transverse field where the…
We assume one site measures without a boundary $e^{-\phi(x)}dx/Z$ that satisfy a log-Sobolev inequality. We prove that if these measures are perturbed with quadratic interactions, then the associated infinite dimensional Gibbs measure on…
Ising model without external field on an infinite Lorentzian triangulation sampled from the uniform distribution is considered. We prove uniqueness of the Gibbs measure in the high temperature region and coexistence of at least two Gibbs…
We extend results on quadratic pressure and convergence of Gibbs mesures from previous joined work of the authors to the Curie-Weiss-Potts model. We define the notion of equilibrium state for the quadratic pressure and show that under some…
We study the electroweak phase transition dynamics with a three-dimensional standard model effective field theory under a gauge-invariant approach. We observe that, at the two-loop level, the phase transition parameters obtained with the…
Given a square box $\Lambda_n\subseteq\mathbb Z^2$ of side length $L^n$ with $L,n>1$, we study hierarchical random fields $\{\phi_x\colon x\in\Lambda_n\}$ with law proportional to ${\rm…
A family of nonequilibrium kinetic Ising models, introduced earlier, evolving under the competing effect of spin flips at {\it zero temperature} and nearest neighbour random spin exchanges is further investigated here. By increasing the…
The notion of Gibbs Measure is used by many researchers of the communities of Mathematical Physics, Probability, Thermodynamic Formalism, Symbolic Dynamics, and others. A natural question is when these several different notions of Gibbs…
The inert doublet model is a well-motivated extension of the Standard Model that contains a dark matter candidate and modifies the dynamics of the electroweak symmetry breaking. In order to detail its phenomenology, we perform a…
Mathematical models in equilibrium statistical mechanics describe physical systems with many particles interacting with an external force and with one another. Gibbs measure is a fundamental concept in this theory. In existing literature…