Related papers: Phase transitions and random matrices
The phase diagram of a system constituted of neutrons and $\Lambda$-hyperons in thermal equilibrium is evaluated in the mean-field approximation. It is shown that this simple system exhibits a complex phase diagram with first and second…
Ecosystems often undergo abrupt regime shifts in response to gradual external changes. These shifts are theoretically understood as a regime switch between alternative stable states of the ecosystem dynamical response to smooth changes in…
We consider self-adjoint unbounded Jacobi matrices with diagonal q_n=n and weights \lambda_n=c_n n, where c_n is a 2-periodical sequence of real numbers. The parameter space is decomposed into several separate regions, where the spectrum is…
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…
In this conference proceeding, I discuss in detail the deconfinement to quark matter that takes place at large densities and/or temperatures. The first-order phase transition that is assumed to appear beyond a critical point gives rise to…
This paper looks at the early theory of phase transitions. It considers a group of related concepts derived from condensed matter and statistical physics. The key technical ideas here go under the names of "singularity", "order parameter",…
Based on numerical simulation and local stability analysis we describe the structure of the phase space of the edge/triangle model of random graphs. We support simulation evidence with mathematical proof of continuity and discontinuity for…
We consider sudden quenches across quantum phase transitions in the $S=1$ XXZ model starting from the Haldane phase. We demonstrate that dynamical phase transitions may occur during these quenches that are identified by nonanalyticities in…
Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties…
We consider the possibility of topological quantum phase transitions of ultracold fermions in optical lattices, which can be studied as a function of interaction strength or atomic filling factor (density). The phase transitions are…
A general procedure for studying finite-N effects in quantum phase transitions of finite systems is presented and applied to the critical-point dynamics of nuclei undergoing a shape-phase transition of second-order (continuous), and of…
Critical transitions, or large changes in the state of a system after a small change in the system's external conditions or parameters, commonly occur in a wide variety of disciplines, from the biological and social sciences to physics.…
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless systems, with say $m$ particles in $N$ single particle states…
Phase transitions and critical behavior of driven systems are reviewed. Models exhibiting phase transitions, spontaneous symmetry breaking, phase separation and coarsening processes in d=1 dimension are discussed.
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
The `random intersection graph with communities' models networks with communities, assuming an underlying bipartite structure of groups and individuals. Each group has its own internal structure described by a (small) graph, while groups…
Turbulence is a widely observed state of fluid flows, characterized by complex, nonlinear interactions between motions across a broad spectrum of length and time scales. While turbulence is ubiquitous, from teacups to planetary atmospheres,…
Many quantum condensed-matter systems, and probably the quantum vacuum of our Universe, are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, physics which emerges in the…
Within the framework of an exactly solvable model, which takes into account the interaction of fluctuating modes with equal and opposite momenta, we consider phase diagrams in systems with coupled scalar order parameters. We show that, in…
Ensembles of random fuzzy non-commutative geometries may be described in terms of finite (\(N^2\)-dimensional) Dirac operators and a probability measure. Dirac operators of type \((p,q)\) are defined in terms of commutators and…