Monte Carlo investigation of a model for a three-dimensional orientational glass with short-range gaussian interaction

Abstract

The analogue of the Edwards-Anderson model for isotropic vector spin glasses, but taking quadrupoles instead of unit vectors at each lattice site of the considered simple cubic lattice, is studied as a model for an orientational glass. We study both the case where the quadrupole moment can orient in a three-dimensional space (m=3) and the case where the orientation is restricted to a plane (m=2), but otherwise the Hamiltonian is fully isotropic. ℋ= $$ - \sum\limits_{\left\langle {i,j} \right\rangle } {J_{ij} } \left[ {\left( {\sum\limits_{\mu = 1}^m {S_i^\mu S_j^\mu } } \right)^2 - \frac{1}{m}} \right]$$ , whereJ ij is a random gaussian interaction between nearest neighbors, andS i μ the μ'th component of them-component unit vectorS i at lattice sitei. We define the analogue of the “nonlinear susceptibility” in spin glasses for the present model and show that it diverges as the temperature is lowered (both casesm=2, andm=3 being consistent with a zero-temperature transition, while form=2 a transition at a nonzero but low temperature cannot be excluded), due to the build-up of long range spatial “squared quadrupolar” correlations. The time-autocorrelation functionq(t) of the quadrupole moments is analyzed in detail and shown to be consistent with the Kohlrausch law,q(t) α exp [−(t/τ) y ], where the relaxation time τ diverges asT→0, while the exponenty vanishes in this limit.