Eur. Phys. J. B (2018) 91: 221
https://doi.org/10.1140/epjb/e2018-90171-0

Regular Article

A projected entropy controller for transition matrix calculations

Department of Physics, University of Waterloo, Waterloo, ON N2L 3G7, Canada

^a e-mail: yevick@uwaterloo.ca

Received: 13 March 2018
Received in final form: 25 April 2018
Published online: 3 October 2018

Abstract

We define the projected entropy S(T) at a given temperature T in the context of an Ising model transition matrix calculation as the entropy associated with the distribution of Markov-chain realizations in energy-magnetization, E–H, space. An even sampling of states is achieved by accumulating the results from multiple Markov chains while decrementing 1∕T at a rate proportional to the inverse of the effective number, exp(S(T)), of accessible projected states. Such a procedure is both highly accurate and far simpler to implement than a previously suggested method based on monitoring the evolution of the E–H distribution at each temperature [D. Yevick, Y.-H. Lee, Eur. Phys. J. B 90, 81 (2017)]. We further demonstrate a transition matrix procedure that instead ensures uniform sampling in physical entropy.