The Edwards-Anderson model of a spin glass is studied by position-space renormalization-group techniques, using an inhomogeneous generalization of Migdal's approximate recursion relation. We treat the spin-1/2 Ising model with independently random nearest-neighbor interactions in dimensionalities $d=2, 3, \mathrm{and} 4$ . The phase diagram, which is in qualitative agreement with mean-field results, exhibits paramagnetic, ferromagnetic, antiferromagnetic, and spin-glass phases. The spin-glass and paramagnetic phases meet along an extended second-order phase boundary, which terminates in two tricritical points. Critical and tricritical exponents are calculated. The spin-glass specific-heat exponent turns out to be large and negative, compatibly with recent experiments which show a rounded specific-heat anomaly.The Edwards-Anderson model of a spin glass is studied by position-space renormalization-group techniques, using an inhomogeneous generalization of Migdal's approximate recursion relation. We treat the spin-1/2 Ising model with independently random nearest-neighbor interactions in dimensionalities $d=2, 3, \mathrm{and} 4$. The phase diagram, which is in qualitative agreement with mean-field results, exhibits paramagnetic, ferromagnetic, antiferromagnetic, and spin-glass phases. The spin-glass and paramagnetic phases meet along an extended second-order phase boundary, which terminates in two tricritical points. Critical and tricritical exponents are calculated. The spin-glass specific-heat exponent turns out to be large and negative, compatibly with recent experiments which show a rounded specific-heat anomaly.

Physical review. B, Solid stateFeb 1, 197784 citations

New Generalizations of Migdal—Kadanoff Bond-Moving Recursion Procedures and Their Applications

Chun-Yang Wang, Wen-Xian Yang, Zhi-Wei Yan +4 more

Considering in symmetrical half-length bond operations, we present in this paper two types of newly-developed generalizations of the remarkable Migdal-Kadanoff bond-moving renormalization group transformation recursion procedures. The predominance in application of these generalized procedures are illustrated by making use of them to study the critical behavior of the spin-continuous Gaussian model constructed on the typical translational invariant lattices and fractals respectively. Results such as the correlation length critical exponents obtained by these means are found to be in good conformity with the classical results from other previous studies.Considering in symmetrical half-length bond operations, we present in this paper two types of newly-developed generalizations of the remarkable Migdal-Kadanoff bond-moving renormalization group transformation recursion procedures. The predominance in application of these generalized procedures are illustrated by making use of them to study the critical behavior of the spin-continuous Gaussian model constructed on the typical translational invariant lattices and fractals respectively. Results such as the correlation length critical exponents obtained by these means are found to be in good conformity with the classical results from other previous studies.

Communications in Theoretical PhysicsApr 1, 20121 citation

d=2, 3, \mathrm{and} 4

. The phase diagram, which is in qualitative agreement with mean-field results, exhibits paramagnetic, ferromagnetic, antiferromagnetic, and spin-glass phases. The spin-glass and paramagnetic phases meet along an extended second-order phase boundary, which terminates in two tricritical points. Critical and tricritical exponents are calculated. The spin-glass specific-heat exponent turns out to be large and negative, compatibly with recent experiments which show a rounded specific-heat anomaly.