arXiv subjects

Royce K. P. Zia

Publications and source records attributed to Royce K. P. Zia.

5 recordsLinked to original sources

arXiv2023

Exact microcanonical statistical analysis of transition behavior in Ising chains and strips

Recent analyses of least-sensitive inflection points in derivatives of the microcanonical entropy for the two-dimensional Ising model revealed higher-order transition signals in addition to the well-studied second-order ferromagnetic/paramagnetic phase transition. In this paper, we re-analyze the exact density of states for the one-dimensional Ising chain as well as the strips with widths/lengths of up to 64/1024 spins, in search of potential transition features. While some transitions begin to emerge as the strip width increases, none are found for the chain, as might be expected.

cond-mat.stat-mech↗

arXiv2014

Modeling interacting dynamic networks: III. Extraordinary properties in a population of extreme introverts and extroverts

Recently, we introduced dynamic networks with preferred degrees, showing that interesting properties are present in a single, homogeneous system as well as one with two interacting networks. While simulations are readily performed, analytic studies are challenging, due mainly to the lack of detailed balance in the dynamics. Here, we consider the two-community case in a special limit: a system of extreme introverts and extroverts - the XIE model. Surprising phenomena appear, even in this minimal model, where the only control parameters are the numbers of each subgroup: $N_{I,E}$. Specifically, an extraordinary transition emerges when $N_I$ crosses $N_E$. For example, the fraction of total number of I-E links jumps from $\thicksim 0$ to $\thicksim 1$. In a $N_I=N_E$ system, this fraction performs a pure random walk so that its distribution displays a flat plateau across most of $[0,1]$, with the edges vanishing as $(N_{I,E})^{-0.38}$ for large systems. Thus, we believe the XIE model exhibits an extreme Thouless effect. For this limiting model, we show that detailed balance is restored and explicitly find the microscopic steady-state distribution. We then use a mean-field approach to find analytic expressions for the degree distributions that are in reasonably good agreement with simulations, provided $N_I$ is not too close to $N_{E}$.

physics.soc-ph↗

arXiv2012

Entrainment and unit velocity: Surprises in an accelerated exclusion process

We introduce a class of distance-dependent interactions in an accelerated exclusion process (AEP) inspired by the observation of transcribing RNA polymerase speeding up when "pushed" by a trailing one. On a ring, the AEP steady state displays a discontinuous transition, from being homogeneous (with augmented currents) to phase-segregated. In the latter state, the holes appear loosely bound and move together, much like a train. Surprisingly, the current-density relation is simply $J=1-ρ$, signifying that the "hole-train" travels with \textit{unit} velocity.

cond-mat.stat-mech↗

arXiv2005

Anomalous nucleation far from equilibrium

We present precision Monte Carlo data and analytic arguments for an asymmetric exclusion process, involving two species of particles driven in opposite directions on a $2 \times L$ lattice. We propose a scenario which resolves a stark discrepancy between earlier simulation data, suggesting the existence of an ordered phase, and an analytic conjecture according to which the system should revert to a disordered state in the thermodynamic limit. By analyzing the finite size effects in detail, we argue that the presence of a single, seemingly macroscopic, cluster is an intermediate stage of a complex nucleation process: In smaller systems, this cluster is destabilized while larger systems allow the formation of multiple clusters. Both limits lead to exponential cluster size distributions which are, however, controlled by very different length scales.

cond-mat.stat-mech↗

arXiv1997

Contrasts between coarsening and relaxational dynamics of surfaces

We discuss static and dynamic fluctuations of domain walls separating areas of constant but different slopes in steady-state configurations of crystalline surfaces both by an analytic treatment of the appropriate Langevin equation and by numerical simulations. In contrast to other situations that describe the dynamics in Ising-like systems such as models A and B, we find that the dynamic exponent z=2 that governs the domain wall relaxation function is not equal to the inverse of the exponent n=1/4 that describes the coarsening process that leads to the steady state.

cond-mat↗