The Scaling Limit for Zero-Temperature Planar Ising Droplets: With and Without Magnetic Fields
Lacoin, Hubert (2014), The Scaling Limit for Zero-Temperature Planar Ising Droplets: With and Without Magnetic Fields, in Ramírez, Alejandro F.; Ben Arous, Gérard; Ferrari, Pablo A.; Newman, Charles M.; Sidoravicius, Vladas; Vares, Maria Eulália, Topics in Percolative and Disordered Systems, Springer : New York, p. 85-120. 10.1007/978-1-4939-0339-9_4
External document linkhttps://arxiv.org/abs/1210.2597v1
Book titleTopics in Percolative and Disordered Systems
Book authorRamírez, Alejandro F.; Ben Arous, Gérard; Ferrari, Pablo A.; Newman, Charles M.; Sidoravicius, Vladas; Vares, Maria Eulália
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Abstract (EN)We consider the continuous time, zero-temperature heat-bath dynamics for the nearest-neighbor Ising model on Z2 with positive magnetic field. For a system of size L∈N, we start with initial condition σ such that σx=−1 if x∈[−L,L]2 and σx=+1 and investigate the scaling limit of the set of • spins when both time and space are rescaled by L. We compare the obtained result and its proof with the case of zero-magnetic fields, for which a scaling result was proved by Lacoin et al. (J Eur Math Soc, in press). In that case, the time-scaling is diffusive and the scaling limit is given by anisotropic motion by curvature.
Subjects / Keywordsheat-bath dynamics; Ising model
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