Parallel-Tempering Monte-Carlo Simulation with Feedback-Optimized Algorithm Applied to a Coil-to-Globule Transition of a Lattice Homopolymer
Lewandowski Krzysztof, Knychała Piotr, Banaszak Michał *
Faculty of Physics, A. Mickiewicz University
ul. Umultowska 85, 61-614 Poznan, Poland
*e-mail: mbanasz@amu.edu.pl
http://www.simgroup.amu.edu.pl
Received:
Received: 15 March 2010; revised: 21 April 2010; accepted: 23 April 2010; published online: 4 May 2010
DOI: 10.12921/cmst.2010.16.01.29-35
OAI: oai:lib.psnc.pl:712
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:
feedback-optimized, Monte Carlo, parallel tempering, polymer, replica exchange, single chain
References:
[1] K. Binder, W. Paul, Macromolecules 41, 4537 (2008).
[2] F. Wang, D.P. Landau, Phys. Rev. Lett. 86, 2050 (2001).
[3] V. Cerny, Journal of Optimization Theory and Applications 45, 41 (1985).
[4] S. Kirkpatrick, C.D. Gelatt Jr., M.P. Vecchi, Science 220, 671 (1983).
[5] R.H. Swendsen, J.S. Wang, Phys. Rev. Let. 57, 2607 (1986).
[6] D.J. Earl, M.W. Deem, Phys. Chem. Chem. Phys. 7, 3910 (2005).
[7] H.G. Katzgraber, S. Trebst, D.A. Huse, M. Troyer, J. Stat. Mech. p. P03018 (2006).
[8] D. Gront, A. Kolinski, J. Phys. Condens. Matter 19 (2007).
[9] D. Sabo, M. Meuwly, D.L. Freeman, J.D. Doll, J. Chem. Phys. 128 (2008).
[10] C. Predescu, M. Predescu, C.V. Ciobanu, J. Phys. Chem. B 109, 4189 (2005).
[11] D.A. Kofke, J. Chem. Phys. 117, 6911 (2002), 120, 206101 (2004).
[12] A. Kone, D.A. Kofke, J. Chem. Phys. 122, 1 (2005).
[13] S. Wołoszczuk, M. Banaszak, P. Knychała, K. Lewandowski, M. Radosz, J. Non-Cryst. Solids 354, 4138 (2008).
[14] K. Lewandowski, P. Knychała, M. Banaszak, Phys. Stat. Sol. B 245, 2524 (2008).
[15] A. Sikorski, Macromolecules 35, 7132 (2002).
[16] N. Rathore, M. Chopra, J.J. de Pablo, J. Chem. Phys. 122, 024111 (2005).
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:
feedback-optimized, Monte Carlo, parallel tempering, polymer, replica exchange, single chain
References:
[1] K. Binder, W. Paul, Macromolecules 41, 4537 (2008).
[2] F. Wang, D.P. Landau, Phys. Rev. Lett. 86, 2050 (2001).
[3] V. Cerny, Journal of Optimization Theory and Applications 45, 41 (1985).
[4] S. Kirkpatrick, C.D. Gelatt Jr., M.P. Vecchi, Science 220, 671 (1983).
[5] R.H. Swendsen, J.S. Wang, Phys. Rev. Let. 57, 2607 (1986).
[6] D.J. Earl, M.W. Deem, Phys. Chem. Chem. Phys. 7, 3910 (2005).
[7] H.G. Katzgraber, S. Trebst, D.A. Huse, M. Troyer, J. Stat. Mech. p. P03018 (2006).
[8] D. Gront, A. Kolinski, J. Phys. Condens. Matter 19 (2007).
[9] D. Sabo, M. Meuwly, D.L. Freeman, J.D. Doll, J. Chem. Phys. 128 (2008).
[10] C. Predescu, M. Predescu, C.V. Ciobanu, J. Phys. Chem. B 109, 4189 (2005).
[11] D.A. Kofke, J. Chem. Phys. 117, 6911 (2002), 120, 206101 (2004).
[12] A. Kone, D.A. Kofke, J. Chem. Phys. 122, 1 (2005).
[13] S. Wołoszczuk, M. Banaszak, P. Knychała, K. Lewandowski, M. Radosz, J. Non-Cryst. Solids 354, 4138 (2008).
[14] K. Lewandowski, P. Knychała, M. Banaszak, Phys. Stat. Sol. B 245, 2524 (2008).
[15] A. Sikorski, Macromolecules 35, 7132 (2002).
[16] N. Rathore, M. Chopra, J.J. de Pablo, J. Chem. Phys. 122, 024111 (2005).
