Related papers: On a Phase Separation Point for One - Dimensional …

Over the last half century the liquid-gas phase transition and the magnetization phase transition have come to be well understood. After an order parameter, $r$, is defined, it can be derived how $r=0$ for $T>T_c$ and how $r \propto (T_c -…

We introduce the point process \begin{align*} \frac{1}{Z_{n}}\prod_{1 \leq j < k \leq n} |e^{i\theta_{j}}+e^{i\theta_{k}}|^{\beta}\prod_{j=1}^{n} d\theta_{j}, \qquad \theta_{1},\ldots,\theta_{n} \in (-\pi,\pi], \quad \beta > 0, \end{align*}…

Regarding metric fluctuations as generating {\it roughness} on the fabric of the otherwise smooth vacuum, it is shown that in its simplest form, the effect can be described by the scalar $\phi^4$ model. The model exhibits a second order…

We study a non-conserved one-dimensional stochastic process which involves two species of particles $A$ and $B$. The particles diffuse asymmetrically and react in pairs as $A\emptyset\leftrightarrow AA\leftrightarrow BA \leftrightarrow…

Phase transition of decay rate from quantum tunneling to thermal activity regimes is investigated in (3+1)-dimensional field theories with symmetry breaking term $f\phi$. By applying the two independent criteria for the sharp first-order…

Phase separation is a fairly common physical phenomenon with examples including the formation of water droplets from humid air (fog, rain), the separation of a crystalline structure from an isotropic material such as a liquid or even the…

The properties of the first-order phase transition in a set of plasma models with common feature - absence of individual correlations between charges of op-posite sign, have been studied. Predicted discontinuities in equilibrium non-uniform…

A model is developed which allows the investigation and classification of the pairing phase transition in atomic nuclei. The regions of the parameter space are discussed for which a pairing phase transition can be observed. The model…

We compare results of the exact field theory of phase separation in two dimensions with Monte Carlo simulations for the $q$-state Potts model with boundary conditions producing an interfacial region separating two pure phases. We confirm in…

We study the relative phase fluctuations of two one-dimensional condensates coupled along their whole extension with a local single-atom interaction. The thermal equilibrium is defined by the competition between independent longitudinal…

The object of this study is a cell model with Curie-Weiss interaction potential. We have already proved the possibility of a mathematically rigorous transition from a continuous system of interacting particles to such a model and made an…

For physical systems described by smooth, finite-range and confining microscopic interaction potentials V with continuously varying coordinates, we announce and outline the proof of a theorem that establishes that unless the equipotential…

The Curie-Weiss Potts model is a mean field version of the well-known Potts model. In this model, the critical line $\beta = \beta_c (h)$ is explicitly known and corresponds to a first order transition when $q > 2$. In the present paper we…

In a field-theoretical context, we consider the Euclidean $(\phi^4+\phi^6)_D$ model compactified in one of the spatial dimensions. We are able to determine the dependence of the transition temperature ($T_{c}$)for a system described by this…

We give a general introduction to quantum phase transitions in strongly-correlated electron systems. These transitions which occur at zero temperature when a non-thermal parameter $g$ like pressure, chemical composition or magnetic field is…

We study the kinetics of the first order phase separation transition in boson-fermion cold-atom mixtures. At sufficiently low temperatures such a transition is driven by quantum fluctuations responsible for the formation of critical nuclei…

We consider a sparse linear regression model Y=X\beta^{*}+W where X has a Gaussian entries, W is the noise vector with mean zero Gaussian entries, and \beta^{*} is a binary vector with support size (sparsity) k. Using a novel conditional…

We consider the point process \begin{align*} \frac{1}{Z_{n}}\prod_{1 \leq j < k \leq n} |e^{i\theta_{j}}-e^{-i\theta_{k}}|^{\beta}\prod_{j=1}^{n} d\theta_{j}, \qquad \theta_{1},\ldots,\theta_{n} \in (-\pi,\pi], \quad \beta > 0, \end{align*}…

In this work we propose a simple example of a one-dimensional thermodynamic system where non-interacting particles are allowed to move over the $[0,1]$ interval, which are influenced by a potential with a fractal structure. We prove that…

Assuming that a quantum field theory with a $\theta$-vacuum term in the action shows non-trivial $\theta$-dependence and provided that some reasonable properties of the probability distribution function of the order parameter hold, we argue…