Related papers: Phases in Large Combinatorial Systems
Dynamical phase transitions are defined as non-analytic points of the large deviation function of current fluctuations. We show that for boundary driven systems, many dynamical phase transitions can be identified using the geometrical…
Our general subject is the emergence of phases, and phase transitions, in large networks subjected to a few variable constraints. Our main result is the analysis, in the model using edge and triangle subdensities for constraints, of a sharp…
We study the asymptotics of large, simple, labeled graphs constrained by the densities of edges and of $k$-star subgraphs, $k\ge 2$ fixed. We prove that under such constraints graphs are "multipodal": asymptotically in the number of…
In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task…
We present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models, where vertices come in different types, and the probability of realizing an edge depends on the types of its…
The phase diagram of a system of monodispersed hard rectangles of size $m\times m k$ on a square lattice is numerically determined for $m=2,3$ and aspect ratio $k= 1,2,\ldots, 7$. We show the existence of a disordered phase, a nematic phase…
We consider a modified graphene model under exchange couplings. Various quantum anomalous phases are known to emerge under uniform or staggered exchange couplings. We introduce the twist between the orientations of two sublattice exchange…
Nuclear matter at finite temperature and barion density exhibits several phase transitions that could happen at the early stages of the Universe evolution and could be realized in heavy-ion or hadron-hadron collisions. Microscopic…
We consider an example of a system with two degrees of freedom admitting separation of variables but having a subset of codimension 1 on which the 2-form defining the symplectic structure degenerates. We show how to use separation of…
Fracton topological phases host fractionalized excitations that are either completely immobile or only mobile along certain lines or planes. We demonstrate how such phases can be understood in terms of two fundamentally different types of…
We study simple models of intermittency, involving switching between two states, within the dynamical large-deviation formalism. Singularities appear in the formalism when switching is cooperative, or when its basic timescale diverges. In…
A microscopic theory is presented for identifying shape-phase structures and transitions in interacting fermion systems. The method provides a microscopic description for collective shape-phases, and reveals detailed dependence of such…
We study the structure of the phase diagram for systems consisting of 2- and 3- level particles dipolarly interacting with a 1-mode electromagnetic field, inside a cavity, paying particular attention to the case of a finite number of…
We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…
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…
The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their…
There has been considerable recent progress in discovering and understanding quantum phases and fluctuations produced by strong correlations. Heavy fermion systems are an ideal platform for systematic studies because low and competing…
The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence…
We study the asymptotics of large, moderate and normal deviations for the connected components of the sparse random graph by the method of stochastic processes. We obtain the logarithmic asymptotics of large deviations of the joint…
Motivated by recent interests in fracton topological phases, we explore the interplay between gapped 2D $\mathbb{Z}_N$ topological phases which admit fractional excitations with restricted mobility and geometry of the lattice on which such…