Related papers: Phase Transitions in the Edge/Concurrent Vertex Mo…
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.…
Exponential family Random Graph Models (ERGMs) can be viewed as expressing a probability distribution on graphs arising from the action of competing social forces that make ties more or less likely, depending on the state of the rest of the…
We propose a family of statistical models for social network evolution over time, which represents an extension of Exponential Random Graph Models (ERGMs). Many of the methods for ERGMs are readily adapted for these models, including…
The ground state of the antiferromagnetic XY model with a kagome lattice is characterized by a well developed accidental degeneracy. As a consequence the phase transition in this system consists in unbinding of pairs of fractional vortices.…
Statistical analysis of social networks provides valuable insights into complex network interactions across various scientific disciplines. However, accurate modeling of networks remains challenging due to the heavy computational burden and…
In this work we employ a simple pairing interaction model in order to study and classify an eventual pairing phase transition in finite fermionic systems. We show that systems with as few as 10-16 fermions can exhibit clear features…
This article develops a class of models called Sender/Receiver Finite Mixture Exponential Random Graph Models (SRFM-ERGMs) that enables inference on networks. This class of models extends the existing Exponential Random Graph Modeling…
We provide a phenomenological theory for topological transitions in restructuring networks. In this statistical mechanical approach energy is assigned to the different network topologies and temperature is used as a quantity referring to…
Stochastic reaction networks are mathematical models frequently used in, but not limited to, biochemistry. These models are continuous-time Markov chains whose transition rates depend on certain parameters called rate constants, which…
Despite the recently exhibited importance of higher-order interactions for various processes, few flexible (null) models are available. In particular, most studies on hypergraphs focus on a small set of theoretical models. Here, we…
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…
We present a detailed study of the evolution of the number of connected components in sub-critical multiplicative random graph processes. We consider a model where edges appear independently after an exponential time at rate equal to the…
We study a new kind of proximity graphs called proportional-edge proximity catch digraphs (PCDs)in a randomized setting. PCDs are a special kind of random catch digraphs that have been developed recently and have applications in statistical…
The main objective of the work presented here is to understand the appearance of phase transitions in pure gauge and scalar lattice QED. Main results are as follows: Pure gauge compact QED with PBC shows a monopole percolation phenomena…
Models for cross-sectional network data have become increasingly well-developed in recent decades, and are widely used. This has led to a growing interest in the connection between such cross-sectional models and the behavioral processes…
A first-order percolation transition, called explosive percolation, was recently discovered in evolution networks with random edge selection under a certain restriction. However, the network percolation with more realistic evolution…
We analyze in detail a second order phase transition that occurs in large N Gaussian multi-matrix models in which the matrices are constrained to be commuting. The phase transition occurs as the relative masses of the matrices are varied,…
Using Monte Carlo simulations, we study thermal and critical properties of two systems, in which domain walls and so-called $Z_2$-vortices as topological defects are presented. The main model is a lattice version of the $O(3)$ principal…
Two types of surface models have been investigated by Monte Carlo simulations on triangulated spheres with compartmentalized domains. Both models are found to undergo a first-order collapsing transition and a first-order surface fluctuation…
The dynamics of weak vs. strong first order phase transitions is investigated numerically for 2+1 dimensional scalar field models. It is argued that the change from a weak to a strong transition is itself a (second order) phase transition,…