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.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.

arXiv:2306.04780Jun 7, 20230 citations

Ising model with long-range interaction

S. H. Florez, M. Roldán

Revista Colombiana de FísicaJan 1, 19970 citations

Linked-Cluster Expansion of the Ising Model

Massimo Campostrini B

arXiv:cond-mat/0005130Journal of Statistical PhysicsApr 1, 200115 citations

Restricted Boltzmann Machine Flows and The Critical Temperature of Ising models

Rodrigo Veiga, Renato Vicente

We explore alternative experimental setups for the iterative sampling (flow) from Restricted Boltzmann Machines (RBM) mapped on the temperature space of square lattice Ising models by a neural network thermometer. This framework has been introduced to explore connections between RBM-based deep neural networks and the Renormalization Group (RG). It has been found that, under certain conditions, the flow of an RBM trained with Ising spin configurations approaches in the temperature space a value around the critical one: $ k_B T_c / J \approx 2.269$. In this paper we consider datasets with no information about model topology to argue that a neural network thermometer is not an accurate way to detect whether the RBM has learned scale invariance or not.We explore alternative experimental setups for the iterative sampling (flow) from Restricted Boltzmann Machines (RBM) mapped on the temperature space of square lattice Ising models by a neural network thermometer. This framework has been introduced to explore connections between RBM-based deep neural networks and the Renormalization Group (RG). It has been found that, under certain conditions, the flow of an RBM trained with Ising spin configurations approaches in the temperature space a value around the critical one: $ k_B T_c / J \approx 2.269$. In this paper we consider datasets with no information about model topology to argue that a neural network thermometer is not an accurate way to detect whether the RBM has learned scale invariance or not.

arXiv:2006.10176Jun 17, 20203 citations

New perspectives on the Ising model

F. Mancini

arXiv:cond-mat/0506117The European Physical Journal BJun 1, 200514 citations

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.