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Europhysics Letters (EPL)

Renormalization Group for the Heisenberg Magnet in a Random Magnetic Field: The Zero-Temperature Fixed Point

Y. S. Parmar

Published May 10, 1994• 0 citations
Publisher

Abstract

Decimation followed by Migdal-Kadanoff bond-moving approximation is used to find critical exponents of Heisenberg model at d = 4 + ε. To first order in ε the modified hyperscaling law ( d - 2 + η)ν = 2 - α is verified. However, there is no dimensional reduction.
DOI
10.1209/0295-5075/26/5/010

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We show that the hyperscaling law is modified whenever the relevant fixed point of the renormalization-group transformation is at zero temperature (infinite coupling). Instead of 2-\ensuremath{\alpha}=d\ensuremath{\nu}, the hyperscaling law now reads 2-\ensuremath{\alpha}=d'\ensuremath{\nu} where d' is the anomalous dimension which is equal to d-\ensuremath{\Vert}y\ensuremath{\Vert} and y is the exponent for the leading irrelevant operator that flows to zero temperature. We discuss the random-field Ising model in detail. We also perform a numerical domain-wall renormalization-group analysis for the d=3 model. For a Gaussian random-field distribution, our results are consistent with a second-order transition at low temperatures, and \ensuremath{\Vert}y\ensuremath{\Vert} is found to be 1.3--1.7. For a \ifmmode\pm\else\textpm\fi{}h distribution, the transition appears to be first order at T=0. .AE
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