arXiv subjects

James Denholm

Publications and source records attributed to James Denholm.

3 recordsLinked to original sources

arXiv2021

High-degeneracy Potts coarsening

I examine the fate of a kinetic Potts ferromagnet with a high ground-state degeneracy that undergoes a deep quench to zero-temperature. I consider single spin-flip dynamics on triangular lattices of linear dimension $8 \le L \le 128$ and set the number of spin states $q$ equal to the number of lattice sites $L \times L$. The ground state is the most abundant final state, and is reached with probability $\approx 0.71$. Three-hexagon states occur with probability $\approx 0.26$, and hexagonal tessellations with more than three clusters form with probabilities of $\mathcal{O}(10^{-3})$ or less. Spanning stripe states -- where the domain walls run along one of the three lattice directions -- appear with probability $\approx 0.03$. "Blinker" configurations, which contain perpetually flippable spins, also emerge, but with a probability that is vanishingly small with the system size.

physics.comp-ph↗

arXiv2020

Anomalous Ising freezing times

We measure the relaxation time of a square lattice Ising ferromagnet that is quenched to zero-temperature from supercritical initial conditions. We reveal an anomalous and seemingly overlooked timescale associated with the relaxation to "frozen" two-stripe states. While close to a power law of the form $\sim L^ν$ , we argue this timescale actually grows as $\sim L^{2}\ln L$, with L the linear dimension of the system. We uncover the mechanism behind this scaling form by using a synthetic initial condition that replicates the late time ordering of two-stripe states, and subsequently explain it heuristically.

cond-mat.stat-mech↗

arXiv2019

Universal behavior in finite 2D kinetic ferromagnets

We study the time evolution of the two-dimensional kinetic Ising model in finite systems with a non-conserved order parameter, considering nearest-neighbour interactions on the square lattice with periodic and open boundary conditions. Universal data collapse in spin product correlation functions is observed which, when expressed in rescaled units, is valid across the entire time evolution of the system at all length scales, not just within the time regime usually considered in the dynamical scaling hypothesis. Consequently, beyond rapidly decaying finite size effects, the evolution of correlations in small finite systems parallels arbitrarily larger cases, even at large fractions of the size of these finite systems.

cond-mat.stat-mech↗