English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study the scalar one-component two-dimensional (2D) $\phi^4$ model bycomputer simulations, with local Metropolis moves. The equilibrium exponents ofthis model are well-established, e.g. for the 2D $\phi^4$ model $\gamma= 1.75$and $\nu= 1$. The model has also been conjectured to belong to the Isinguniversality class. However, the value of the critical dynamical exponent $z_c$is not settled. In this paper, we obtain $z_c$ for the 2D $\phi^4$ model usingtwo independent methods: (a) by calculating the relative terminal exponentialdecay time $\tau$ for the correlation function $\langle \phi(t)\phi(0)\rangle$,and thereafter fitting the data as $\tau \sim L^{z_c}$, where $L$ is the systemsize, and (b) by measuring the anomalous diffusion exponent for the orderparameter, viz., the mean-square displacement (MSD) $\langle \Delta\phi^2(t)\rangle\sim t^c$ as $c=\gamma/(\nu z_c)$, and from the numericallyobtained value $c\approx 0.80$, we calculate $z_c$. For different values of thecoupling constant $\lambda$, we report that $z_c=2.17\pm0.03$ and$z_c=2.19\pm0.03$ for the two methods respectively. Our results indicate that$z_c$ is independent of $\lambda$, and is likely identical to that for the 2DIsing model. Additionally, we demonstrate that the Generalised LangevinEquation (GLE) formulation with a memory kernel, identical to those applicablefor the Ising model and polymeric systems, consistently capture the observedanomalous diffusion behavior.

Critical Dynamical Exponent of the Two-Dimensional Scalar $\phi^4$ Model with Local Moves