Year: 2018
Type: article
Abstract: We study the scalar one-component two-dimensional (2D) ${\ensuremath{\phi}}^{4}$ model by computer simulations, with local Metropolis moves. The equilibrium exponents of this model are well established, e.g., for the 2D ${\ensuremath{\phi}}^{4}$ model $\ensuremath{\gamma}=1.75$ and $\ensuremath{\nu}=1$. The model has also been conjectured to belong to the Ising universality class. However, the value of the critical dynamical exponent ${z}_{c}$ is not settled. In this paper, we obtain ${z}_{c}$ for the 2D ${\ensuremath{\phi}}^{4}$ model using two independent methods: (a) by calculating the relative terminal exponential decay time $\ensuremath{\tau}$ for the correlation function $\ensuremath{\langle}\mathrm{\ensuremath{\Phi}}(t)\mathrm{\ensuremath{\Phi}}(0)\ensuremath{\rangle}$, and thereafter fitting the data as $\ensuremath{\tau}\ensuremath{\sim}{L}^{{z}_{c}}$, where $L$ is the system size, and (b) by measuring the anomalous diffusion exponent for the order parameter, viz., the mean-square displacement $\ensuremath{\langle}\mathrm{\ensuremath{\Delta}}{\mathrm{\ensuremath{\Phi}}}^{2}(t)\ensuremath{\rangle}\ensuremath{\sim}{t}^{c}$ as $c=\ensuremath{\gamma}/(\ensuremath{\nu}{z}_{c})$, and from the numerically obtained value $c\ensuremath{\approx}0.80$, we calculate ${z}_{c}$. For different values of the coupling constant $\ensuremath{\lambda}$, we report that ${z}_{c}=2.17\ifmmode\pm\else\textpm\fi{}0.03$ and ${z}_{c}=2.19\ifmmode\pm\else\textpm\fi{}0.03$ for the two methods, respectively. Our results indicate that ${z}_{c}$ is independent of $\ensuremath{\lambda}$, and is likely identical to that for the 2D Ising model. Additionally, we demonstrate that the generalized Langevin equation formulation with a memory kernel, identical to those applicable for the Ising model and polymeric systems, consistently captures the observed anomalous diffusion behavior.
Source: Physical review. E
Institutions: Utrecht University, University of Warwick
Language: Latvian
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
Funder: China Scholarship Council
OpenAlex ID: W2884819920