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arXiv:2306.04780

A nonequilibrium system on a restricted scale-free network

Rafael Alves Dumer, Marta Arantes Godoy

Published Jun 7, 2023• 0 citations
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Abstract

The nonequilibrium Ising model on a restricted scale-free network has been studied with one- and two-spin flip competing dynamics employing Monte Carlo simulations. The dynamics present in the system can be defined by the probability $q$ in which the one-spin flip process simulate the contact with a heat bath at a given temperature $T$, and with a probability ($1-q$) the two-spin flip process mimics the system subjected to an external flux of energy into it. The system network is described by a power-law degree distribution in the form $P(k)\sim k^{-α}$, and the restriction is made by fixing the maximum, $k_{m}$, and minimum, $k_{0}$, degree on distribution for the whole network size. This restriction keeps finite the second and fourth moment of degree distribution, allowing us to obtain a finite critical point for any value of $α$. For these critical points, we have calculated the thermodynamic quantities of the system, such as, the total ${m}_{N}^{F}$ and staggered ${m}_{N}^{AF}$ magnetizations per spin, susceptibility $χ_{N}$, and reduced fourth-order Binder cumulant ${U}_{N}$, for several values of lattice size $N$ and exponent $1\leα\le5$. Therefore, the phase diagram was built and a self-organization phenomena is observed from the transitions between antiferromagnetic AF to paramagnetic P, and P to ferromagnetic F phases. Using the finite-size scaling theory, we also obtained the critical exponents for the system, and a mean-field critical behavior is observed, exhibiting the same universality class of the system on the equilibrium and out of it.

DOI
10.48550/arxiv.2306.04780

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In this paper we study finite-size scaling at criticality in the Gibbs ensemble with Monte Carlo simulations. A recent lattice-gas version of Gibbs-ensemble sampling for the two-dimensional Ising-model magnet with nearest-neighbor ferromagnetic interactions on two subsystems of L\ifmmode\times\else\texttimes\fi{}L lattices is considered. Both square and triangular lattices with a range of lattice sizes are simulated at bulk criticality. We are interested in the question of universality for the fourth-order cumulant of the order-parameter distribution in the Gibbs ensemble. Estimates of -1.954\ifmmode\pm\else\textpm\fi{}0.005 and -1.9543\ifmmode\pm\else\textpm\fi{}0.005 are obtained for the square and triangular lattices, respectively. These values confirm universality within the Gibbs ensemble, but are statistically different from the canonical-ensemble values of \ensuremath{\sim}-1.83. We point out that one must interpret this apparent ensemble dependence with care. Unlike in the canonical ensemble, the order parameter in the Gibbs ensemble is the subsystem magnetization. Its fourth-order cumulant is not simply related to the usual fourth magnetic-field derivative of the total free energy. Standard finite-size scaling analysis of data for the total specific heat, subsystem magnetization, and susceptibility are also considered and found to be in good agreement with finite-size scaling.
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