Vector spin glasses with random short-range anisotropic couplings are studied using the defect-wall renormalization-group method. By calculating the correlation length exponent \ensuremath{\nu} and the fractal dimension of the defect wall, ${\mathit{d}}_{\mathit{s}}$ , we obtain the first direct evidence that in two dimensions these systems have a zero-temperature transition in the same universality class as the Ising spin glass. We also present results which strongly suggest that these systems have a transition at nonzero temperature in three dimensions.Vector spin glasses with random short-range anisotropic couplings are studied using the defect-wall renormalization-group method. By calculating the correlation length exponent \ensuremath{\nu} and the fractal dimension of the defect wall, ${\mathit{d}}_{\mathit{s}}$, we obtain the first direct evidence that in two dimensions these systems have a zero-temperature transition in the same universality class as the Ising spin glass. We also present results which strongly suggest that these systems have a transition at nonzero temperature in three dimensions.

Physical Review LettersSep 6, 199319 citations

Scaling theory of the ordered phase of spin glasses

Alan J. Bray, M A Moore

Lecture notes in physicsJan 1, 198782 citations

Critical exponents of the U ( n ) vector spin glasses

J Stein

The critical exponents of the classical spin glasses with O ( m − 2 n )⊗ U ( n ) symmetry are obtained to order 2 of the -expansion around six dimensions, where = 6 − d . This new unitary symmetry is realized in the m -vector ( m ⩾ 2) spin glasses with anisotropic quenched random Dzyaloshinskii-Moriya (DM) interaction. Such a random DM interaction with n correlated couplings leads to critical exponents which are different from those of any isotropic m -vector spin glass and thus belong to new universality classes.The critical exponents of the classical spin glasses with O ( m − 2 n )⊗ U ( n ) symmetry are obtained to order 2 of the -expansion around six dimensions, where = 6 − d . This new unitary symmetry is realized in the m -vector ( m ⩾ 2) spin glasses with anisotropic quenched random Dzyaloshinskii-Moriya (DM) interaction. Such a random DM interaction with n correlated couplings leads to critical exponents which are different from those of any isotropic m -vector spin glass and thus belong to new universality classes.

Europhysics Letters (EPL)Jun 20, 19962 citations

A study of short-range spin glasses

Haim Sompolinsky, Annette Zippelius

Lecture notes in physicsJan 1, 19830 citations

Damage Spreading in ±J Asymmetric Ising Spin Glasses

Rita M. C. de Almeida, L. Bernadi, Ian A. Campbell

Spin glasses in dimensions 2, 3, 4 and mean field are studied numerically as a function of the degree of asymmetry of the interactions between spins. Damage spreading data are used to assess the effects on the spin glass ordering of introducing asymmetry in the couplings. In all dimensions the critical temperature for damage spreading is rather insensitive to the asymmetry, but the spin glass ordering is strongly suppressed by any finite degree of asymmetry. We discuss the physical significance of the damage spreading parameter.Spin glasses in dimensions 2, 3, 4 and mean field are studied numerically as a function of the degree of asymmetry of the interactions between spins. Damage spreading data are used to assess the effects on the spin glass ordering of introducing asymmetry in the couplings. In all dimensions the critical temperature for damage spreading is rather insensitive to the asymmetry, but the spin glass ordering is strongly suppressed by any finite degree of asymmetry. We discuss the physical significance of the damage spreading parameter.

Journal de Physique IMar 1, 19953 citations

{\mathit{d}}_{\mathit{s}}

, we obtain the first direct evidence that in two dimensions these systems have a zero-temperature transition in the same universality class as the Ising spin glass. We also present results which strongly suggest that these systems have a transition at nonzero temperature in three dimensions.