2015/08/04 by Roy Cerqueti, Cerqueti, Roy, Emilio De Santis +1
Mathematics · Physics and Astronomy · #60K35 #82B44 #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1508.00850
openalex publication_date 2015/08/04 · openalex created_date 2023/02/16 · openalex updated_date 2026/07/28
This paper deals with the stochastic Ising model with a temperature shrinking\nto zero as time goes to infinity. A generalization of the Glauber dynamics is\nconsidered, on the basis of the existence of simultaneous flips of some spins.\nSuch dynamics act on a wide class of graphs which are periodic and embedded in\n\ℝd. The interactions between couples of spins are assumed to be\nquenched i.i.d. random variables following a Bernoulli distribution with\nsupport -1,+1 . The specific problem here analyzed concerns the assessment\nof how often (finitely or infinitely many times, almost surely) a given spin\nflips. Adopting the classification proposed in citeGNS, we present\nconditions in order to have models of type \F (any spin flips\nfinitely many times), \I (any spin flips infinitely many times) and\n\M (a mixed case). Several examples are provided in all dimensions\nand for different cases of graphs. The most part of the obtained results holds\ntrue for the case of zero-temperature and some of them for the cubic lattice\n mathbbLd=(\ℤd, \𝔼d) as well.\n