TY - JOUR

T1 - Real space renormalization group approach to the random field Ising model

AU - Dayan, I.

AU - Schwartz, M.

AU - Young, A. P.

PY - 1993

Y1 - 1993

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=21144470981&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/26/13/014

DO - 10.1088/0305-4470/26/13/014

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AN - SCOPUS:21144470981

SN - 0305-4470

VL - 26

SP - 3093

EP - 3103

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 13

M1 - 014

ER -