Parallel-Tempering Monte-Carlo Simulation with Feedback-Optimized Algorithm Applied to a Coil-to-Globule Transition of a Lattice Homopolymer

Abstract

Abstract:We present a study of the parallel tempering (replica exchange) Monte Carlo method, with special focus on the feedbackoptimized parallel tempering algorithm, used for generating an optimal set of simulation temperatures. This method is applied to a lattice simulation of a homopolymer chain undergoing a coil-to-globule transition upon cooling. We select the optimal number of replicas for different chain lengths, N = 25, 50 and 75, using replica's round-trip time in temperature space, in order to determine energy, specific heat, and squared end-to-end distance of the homopolymer chain for the selected temperatures. We also evaluate relative merits of this optimization method. Key words: Monte Carlo, parallel tempering, replica exchange, feedback-optimized, polymer, single chain CMST 16(1) 29-35 (201029-35 ( ) DOI:10.12921/cmst.2010 K. Lewandowski, P. Knychała, M. Banaszak 30and exchange interval, S. It is known that quality of the PT method strongly depends on those parameters, and if they are not chosen correctly, simulation can give the same results as without the PT. It is not clear how many replicas are optimal, and it is hard to establish the appropriate criteria for this choice. One approach is to consider some thermodynamic quantity (for example the specific heat, C v ) and to test it how much CPU-time is needed to obtain correct result, or run many simulations with the same number of MCS (or total MCS of all replicas), and to test measurement accuracy for this quantity. In another approach, one can find the optimum * T set that gives the shortest round-trip times of replicas in temperature space.Feedback-optimized PT (FOPT) algorithm, which we use in this work, is designed to find temperature sets that maximize the current of replicas from the lowest temperature to the highest one (details in reference [7] The FOPT uses ( )f T histogram to optimize temperature set in order to minimize round-trip times.In this work, we use round-trip time to find optimal parameters set. We test systems of different sizes, N, and with different number of replicas, M, to find the optimum parameter set. We do not vary the exchange interval, S, which is set to 200 MCS. In the future, we intend to test the S effect on the PT simulation results.It is worth to notice, that there are also other methods for generating optimal temperature sets [8][9][10]. One of them, is proposed by Sabe et al. [9], and is based mainly on the work of Kofke [11] and Kone and Kofke [12], in which the optimal temperature sets are found by using the condition of constant entropy increase for the adjacent replicas. According to our knowledge, the round-trip time of replicas with the FOPT, which we present in this work, is used as a criterion for finding optimal number of replicas in the PT simulations for the first time. II. MODELThe simulation is performed on the face centered cubic (FCC) lattice with coordination number z = 12 and the bond length 2 l a = where a is the FCC lattice constant. Chain bond are not allowed to be stretched or br...

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