Real space renormalization group approach to the random field Ising model

I. Dayan*, M. Schwartz, A. P. Young

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The authors discuss results from two types of real space renormalization group (RSRG) calculations applied to the random field Ising model in three dimensions. Starting from a lattice of size L, the RSRG is used to reduce the lattice to a size L=2, on which the trace is done exactly. In this way, thermodynamic properties, such as the magnetization and susceptibility, can be determined approximately. They find that, for a given size, the susceptibility increases as the temperature, T, is reduced down to the transition temperature, Tc, and becomes essentially independent of temperature below T c. Both in the vicinity of Tc and at lower temperatures, there are large sample-to-sample fluctuations in the susceptibility which grow with increasing system size. They interpret these results in terms of the droplet theory of the transition.

Original languageEnglish
Article number014
Pages (from-to)3093-3103
Number of pages11
JournalJournal of Physics A: Mathematical and General
Issue number13
StatePublished - 1993


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