Computation of latent heat in the system of multi-component order parameter: 3D Ashkin-Teller model
Jeziorek-Knioła Dorota, Wojtkowiak Zbigniew, Musiał Grzegorz *
Adam Mickiewicz University
Faculty of Physics
ul. Umultowska 85
61-614 Poznań, Poland
*E-mail: gmusial@amu.edu.pl
Received:
Received: 13 November 2018; revised: 29 March 2019; accepted: 29 March 2019; published online: 31 March 2019
DOI: 10.12921/cmst.2018.0000053
Abstract:
The method for computing the latent heat in a system with many independently behaving components of the order parameter proposed previously is presented for a chosen point of the phase diagram of the 3D Ashkin-Teller (AH) model. Binder, Challa, and Lee-Kosterlitz cumulants are exploited and supplemented by the use of the energy distribution histogram. The proposed computer experiments using the Metropolis algorithm calculate the cumulants in question, the internal energy and its partial contributions as well as the energy distribution for the model Hamiltonian and its components. The important part of our paper is an attempt to validate the results obtained by several independent methods.
Key words:
high performance computing, latent heat, temperature driven phase transitions, the standard 3D Ashkin-Teller model
References:
[1] K. Binder, D. P. Landau, Phys. Rev. B 30, 1477 (1984).
[2] M. S. S. Challa, D. P. Landau, K. Binder, Phys. Rev. B 34, 1841 (1986).
[3] J. Lee, J. M. Kosterlitz, Phys. Rev. B 43, 3265 (1991).
[4] D. Jeziorek-Knioła, Z. Wojtkowiak, G. Musiał, Acta Phys. Polon. A 133, 435 (2018).
[5] J. Ashkin, E. Teller, Phys. Rev. 64, 178 (1943).
[6] J. P. Santos, F. C. Sá Barreto, Braz. J. Phys. 46, 70 (2016).
[7] Ü. Akıncı, Physica A 469, 740 (2017).
[8] J. P. Santos, D. S. Rosa, F. C. Sá Barreto, Phys. Lett. A 382, 272 (2018).
[9] R. V. Ditzian, J. R. Banavar, G. S. Grest, L. P. Kadanoff, Phys. Rev. B 22, 2542 (1980).
[10] G. Musiał, Phys. Rev. B 69, 024407 (2004).
[11] G. Musiał, J. Rogiers, Phys. Status Solidi B 243, 335 (2006).
[12] Z. Wojtkowiak, G. Musiał, Physica A 513, 104 (2019).
[13] R. J. Baxter, Exactly Solvable Models in Statistical Mechanics (Academic Press, London, 1982).
[14] M. S. Gronsleth, T. B. Nilssen, E. K. Dahl, E. B. Stiansen, C. M. Varma, A. Sudbo, Phys. Rev. B 79, 094506 (2009).
[15] A. Giuliani, V. Mastropietro, Comm. in Math. Phys. 256, 681 (2005); V. Mastropietro, Non-Perturbative Renormalization (World Scientific, London, 2008).
[16] S. Wiseman, E. Domany, Phys. Rev. E 51, 3074 (1995).
[17] C. Fan, Phys. Lett. 39A, 136 (1972).
[18] D. Jeziorek-Knioła, G. Musiał, L. De¸bski, J. Rogiers, S. Dylak, Acta Phys. Polon. A 121, 1105 (2012).
[19] D. Jeziorek-Knioła, G. Musiał, Z. Wojtkowiak, Acta Phys. Polon. A 127, 327 (2015).
[20] G. Musiał, L. De¸bski, G. Kamieniarz, Phys. Rev. B 66, 012407 (2002).
[21] G. Szukowski, G. Kamieniarz, G. Musiał, Phys. Rev. E 77, 031124 (2008).
[22] W. Janke, Lect. Notes in Phys. 739, 79 (2008).
[23] W. Janke, in Computer Simulations of Surfaces and Interfaces, ed. by B. Dünweg, D. P. Landau, A. I. Milchev, NATO Science Series, II. Math., Phys. Chem. 114, pp. 111-136 (2003).
[24] K. Binder, Rep. Prog. Phys. 60, 487 (1997).
[25] M. Mueller, W. Janke, D. A. Johnston, Phys. Rev. Lett. 112, 200601 (2014).
The method for computing the latent heat in a system with many independently behaving components of the order parameter proposed previously is presented for a chosen point of the phase diagram of the 3D Ashkin-Teller (AH) model. Binder, Challa, and Lee-Kosterlitz cumulants are exploited and supplemented by the use of the energy distribution histogram. The proposed computer experiments using the Metropolis algorithm calculate the cumulants in question, the internal energy and its partial contributions as well as the energy distribution for the model Hamiltonian and its components. The important part of our paper is an attempt to validate the results obtained by several independent methods.
Key words:
high performance computing, latent heat, temperature driven phase transitions, the standard 3D Ashkin-Teller model
References:
[1] K. Binder, D. P. Landau, Phys. Rev. B 30, 1477 (1984).
[2] M. S. S. Challa, D. P. Landau, K. Binder, Phys. Rev. B 34, 1841 (1986).
[3] J. Lee, J. M. Kosterlitz, Phys. Rev. B 43, 3265 (1991).
[4] D. Jeziorek-Knioła, Z. Wojtkowiak, G. Musiał, Acta Phys. Polon. A 133, 435 (2018).
[5] J. Ashkin, E. Teller, Phys. Rev. 64, 178 (1943).
[6] J. P. Santos, F. C. Sá Barreto, Braz. J. Phys. 46, 70 (2016).
[7] Ü. Akıncı, Physica A 469, 740 (2017).
[8] J. P. Santos, D. S. Rosa, F. C. Sá Barreto, Phys. Lett. A 382, 272 (2018).
[9] R. V. Ditzian, J. R. Banavar, G. S. Grest, L. P. Kadanoff, Phys. Rev. B 22, 2542 (1980).
[10] G. Musiał, Phys. Rev. B 69, 024407 (2004).
[11] G. Musiał, J. Rogiers, Phys. Status Solidi B 243, 335 (2006).
[12] Z. Wojtkowiak, G. Musiał, Physica A 513, 104 (2019).
[13] R. J. Baxter, Exactly Solvable Models in Statistical Mechanics (Academic Press, London, 1982).
[14] M. S. Gronsleth, T. B. Nilssen, E. K. Dahl, E. B. Stiansen, C. M. Varma, A. Sudbo, Phys. Rev. B 79, 094506 (2009).
[15] A. Giuliani, V. Mastropietro, Comm. in Math. Phys. 256, 681 (2005); V. Mastropietro, Non-Perturbative Renormalization (World Scientific, London, 2008).
[16] S. Wiseman, E. Domany, Phys. Rev. E 51, 3074 (1995).
[17] C. Fan, Phys. Lett. 39A, 136 (1972).
[18] D. Jeziorek-Knioła, G. Musiał, L. De¸bski, J. Rogiers, S. Dylak, Acta Phys. Polon. A 121, 1105 (2012).
[19] D. Jeziorek-Knioła, G. Musiał, Z. Wojtkowiak, Acta Phys. Polon. A 127, 327 (2015).
[20] G. Musiał, L. De¸bski, G. Kamieniarz, Phys. Rev. B 66, 012407 (2002).
[21] G. Szukowski, G. Kamieniarz, G. Musiał, Phys. Rev. E 77, 031124 (2008).
[22] W. Janke, Lect. Notes in Phys. 739, 79 (2008).
[23] W. Janke, in Computer Simulations of Surfaces and Interfaces, ed. by B. Dünweg, D. P. Landau, A. I. Milchev, NATO Science Series, II. Math., Phys. Chem. 114, pp. 111-136 (2003).
[24] K. Binder, Rep. Prog. Phys. 60, 487 (1997).
[25] M. Mueller, W. Janke, D. A. Johnston, Phys. Rev. Lett. 112, 200601 (2014).
