Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physics
A Percolation-Theoretic Approach To Spin Glass Phase Transitions, Jonathan Machta, C. M. Newman, D. L. Stein
A Percolation-Theoretic Approach To Spin Glass Phase Transitions, Jonathan Machta, C. M. Newman, D. L. Stein
Jonathan Machta
The magnetically ordered, low temperature phase of Ising ferromagnets is manifested within the associated Fortuin—Kasteleyn (FK) random cluster representation by the occurrence of a single positive density percolating cluster. In this paper, we review our recent work on the percolation signature for Ising spin glass ordering — both in the short-range Edwards—Anderson (EA) and infinite-range Sherrington—Kirkpatrick (SK) models — within a tworeplica FK representation and also in the different Chayes—Machta—Redner two-replica graphical representation. Numerical studies of the ±J EA model in dimension three and rigorous results for the SK model are consistent in supporting the conclusion that the signature of …
Strengths And Weaknesses Of Parallel Tempering, Jonathan Machta
Strengths And Weaknesses Of Parallel Tempering, Jonathan Machta
Jonathan Machta
Parallel tempering, also known as replica exchange Monte Carlo, is studied in the context of two simple free-energy landscapes. The first is a double-well potential defined by two macrostates separated by a barrier. The second is a “golf course” potential defined by microstates having two possible energies with exponentially more high-energy states than low-energy states. The equilibration time for replica exchange is analyzed for both systems. For the double-well system, parallel tempering with a number of replicas that scales as the square root of the barrier height yields exponential speedup of the equilibration time. On the other hand, replica exchange …