TY - JOUR

T1 - Critical properties of a simple soluble spin glass model

AU - Aharony, A.

AU - Imry, Y.

N1 - Funding Information:
THE THEORY of phase transition in quenched magnetic systems with random exchange interactions has recently drawn much attention.1 A special class of such phase transitions involves the spin glass ordered phase, in which the local magnetic moments are frozen in random directions, exhibiting no long range order. Experimentally, the most commonly investigated spin glasses are dilute substitutional magnetic alloys, e.g. CuMn or AuFe.3 These exhibit definite anomalies including the non vanishing of a spin glass order parameter, e.g. = (S)I or Q = 1(5\>12 ((S\>is the thermal average of the spin at a given random configuration of exchange couplings or site occupations, and the bar denotes averaging over configurations) below some temperature,4’5 a cusp in the magnetic susceptibility, probably some anomalies in the specific heat and in the electrical resistivity,6 and the disappearance of these anomalies at a finite magnetic field.5 Theoretically, one must calculate the free energy of the spin glass as the configurational average of the free energies for fixed random configurations. One assumes random exchange bonds”õr random site occupation,~~dsucthhat the average exchange is small, and uses some trick to obtain this configurational average. Common tricks include averaging the n’th power of the partition function and t8akoirnignththeelriem-it normalization group approach,9 modified “mean-random-field-approximation ,10 computer simulations,2 ~ and the theory of random matrices.11 None of these theories gives accurate results at realistic dimensionalities, due either to the neglect of fluctuations8’1°or to an e-expansion near d = 6.~ * Supported by a grant from the United States—Israel Binational Science Foundation (BSF), Jerusalem, Israel.

PY - 1976/1/1

Y1 - 1976/1/1

N2 - An exactly soluble model, in which a random exchange ± J and uniform field B can be transformed into a uniform exchange and a random magnetic field, ± B, is studied. At B = 0, the model exhibits a spin glass ordered phase, for which all critical exponents are derived. In particular, the magnetic susceptibility exhibits a cusp and its divergent second derivative is related to long range correlations of a spin glass order parameter. At B ≠ 0, the thermodynamic singularities disappear for isotropic (Ising) systems at dimensions d < 4(2), and are distinct from those at B = 0 for 6 > d > 4(2). A more general scaling theory is formulated for B → 0.

AB - An exactly soluble model, in which a random exchange ± J and uniform field B can be transformed into a uniform exchange and a random magnetic field, ± B, is studied. At B = 0, the model exhibits a spin glass ordered phase, for which all critical exponents are derived. In particular, the magnetic susceptibility exhibits a cusp and its divergent second derivative is related to long range correlations of a spin glass order parameter. At B ≠ 0, the thermodynamic singularities disappear for isotropic (Ising) systems at dimensions d < 4(2), and are distinct from those at B = 0 for 6 > d > 4(2). A more general scaling theory is formulated for B → 0.

UR - http://www.scopus.com/inward/record.url?scp=49549127926&partnerID=8YFLogxK

U2 - 10.1016/0038-1098(76)91301-6

DO - 10.1016/0038-1098(76)91301-6

M3 - Article

AN - SCOPUS:49549127926

SN - 0038-1098

VL - 20

SP - 899

EP - 903

JO - Solid State Communications

JF - Solid State Communications

IS - 9

ER -