Spin Glass Stiffness in zero Dimensions
Stefan Boettcher (Emory U)
TL;DR
This paper derives an analytical expression for the spin glass stiffness in zero dimensions, revealing that the stiffness exponent y_0 equals -1, consistent with one-dimensional results, thereby completing the understanding across dimensions.
Contribution
It provides the first analytical derivation of the spin glass stiffness exponent in zero dimensions for the Migdal-Kadanoff lattice.
Findings
The stiffness exponent y_0 in zero dimensions is -1.
The result aligns with the one-dimensional case.
Completes the dimensional analysis of spin glass stiffness.
Abstract
A unique analytical result for the Migdal-Kadanoff hierarchical lattice is obtained. The scaling of the defect energy for a zero-dimensional spin glass is derived for a bond distribution that is continuous at the origin. The value of the ``stiffness'' exponent in zero dimensions, y_0=-1, corresponds to the value also found in one dimension. This result complements and completes earlier findings for y_d at d>0.
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