Chin. Phys. Lett.  2024, Vol. 41 Issue (10): 100502    DOI: 10.1088/0256-307X/41/10/100502
GENERAL |
Complete Universal Scaling in First-Order Phase Transitions
Fan Zhong*
School of Physics and State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510275, China
Cite this article:   
Fan Zhong 2024 Chin. Phys. Lett. 41 100502
Download: PDF(633KB)   PDF(mobile)(681KB)   HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract Phase transitions and critical phenomena are among the most intriguing phenomena in nature and society. They are classified into first-order phase transitions (FOPTs) and continuous ones. While the latter shows marvelous phenomena of scaling and universality, whether the former behaves similarly is a long-standing controversial issue. Here we definitely demonstrate complete universal scaling in field driven FOPTs for Langevin equations in both zero and two spatial dimensions by rescaling all parameters and subtracting nonuniversal contributions with singular dimensions from an effective temperature and a special field according to an effective theory. This offers a perspective different from the usual nucleation and growth but conforming to continuous phase transitions to study FOPTs.
Received: 13 August 2024      Editors' Suggestion Published: 26 September 2024
PACS:  05.70.Fh.  
  64.60.-i (General studies of phase transitions)  
  64.60.My (Metastable phases)  
  75.40.Gb (Dynamic properties?)  
TRENDMD:   
URL:  
https://cpl.iphy.ac.cn/10.1088/0256-307X/41/10/100502       OR      https://cpl.iphy.ac.cn/Y2024/V41/I10/100502
Service
E-mail this article
E-mail Alert
RSS
Articles by authors
Fan Zhong
[1] Fisher M E 1967 Physics 3 255
[2]Gunton J D, San Miguel M, and Sahni P S 1983 The Dynamics of First-Order Phase Transitions. In: Phase Transitions and Critical Phenomena eds Domb C and Lebowitz J L vol 8 p 267 (London: Academic)
[3] Binder K 1987 Rep. Prog. Phys. 50 783
[4]Binder K and Fratzl P 2001 Phase Transformations in Materials ed Kostorz G pp 409–480 (Weinheim: Wiley)
[5] Binder K and Virnau P 2016 J. Chem. Phys. 145 211701
[6]Stanley H E 1971 Introduction to Phase Transitions and Critical Phenomena (Oxford: Oxford University Press)
[7]Ma S K 1976 Modern Theory of Critical Phenomena (Canada: W. A. Benjamin Inc.)
[8]Cardy J 1996 Scaling and Renormalization in Statistical Physics (Cambridge: Cambridge University Press)
[9]Zinn-Justin J 2021 Quantum Field Theory and Critical Phenomena 5th edn (Oxford: Oxford University Press)
[10]Amit D J and Martin-Mayer V 2005 Field Theory, the Renormalization Group, and Critical Phenomena 3rd edn (Singapore: World Scientific)
[11] Oxtoby D W 1998 Acc. Chem. Res. 31 91
[12] Gunton J D 1999 J. Stat. Phys. 95 903
[13] Auer S and Frenkel D 2004 Annu. Rev. Phys. Chem. 55 333
[14] Sear R P 2007 J. Phys.: Condens. Matter 19 033101
[15] Filion L, Ni R, Frenkel D, and Dijkstra M 2011 J. Chem. Phys. 134 134901
[16] Zhong F 2018 J. Phys.: Condens. Matter 30 445401
[17] Nienhuis B and Nauenberg M 1975 Phys. Rev. Lett. 35 477
[18] Fisher M E and Berker A N 1982 Phys. Rev. B 26 2507
[19] Binder K and Landau D P 1984 Phys. Rev. B 30 1477
[20] Borgs C and Kotecky R 1990 J. Stat. Phys. 61 79
[21] Marro J, Lebowitz J L, and Kalos M H 1979 Phys. Rev. Lett. 43 282
[22] Bray A J 2002 Adv. Phys. 51 481
[23]Zhang J X and Li X J 1985 Acta Scientiarum Naturalium Universitatis SunYatSeni 23 45 (in Chinese)
[24] Zhang J X, Fung P C W, and Zeng W G 1995 Phys. Rev. B 52 268
[25] Zhang J X, Yang Z H, and Fung P C W 1995 Phys. Rev. B 52 278
[26] Schülke L and Zheng B 2000 Phys. Rev. E 62 7482
[27] Iino S, Morita S, Kawashima N, and Sandvik A W 2019 J. Phys. Soc. Jpn. 88 034006
[28] Rao M, Krishnamurthy H R, and Pandit R 1990 Phys. Rev. B 42 856
[29] Lo W S and Pelcovits R A 1990 Phys. Rev. A 42 7471
[30] Dhar D and Thomas P B 1992 J. Phys. A 25 4967
[31] Jung P, Gray G, Roy R, and Mandel P 1990 Phys. Rev. Lett. 65 1873
[32] Rao M and Pandit R 1991 Phys. Rev. B 43 3373
[33] Sengupta S, Marathe Y, and Puri S 1992 Phys. Rev. B 45 7828
[34] Somoza A M and Desai R C 1993 Phys. Rev. Lett. 70 3279
[35] Mahato M C and Shenoy S R 1993 J. Stat. Phys. 73 123
[36] Thomas P B and Dhar D 1993 J. Phys. A 26 3973
[37] He Y L and Wang G C 1993 Phys. Rev. Lett. 70 2336
[38] Luse C N and Zangwill A 1994 Phys. Rev. E 50 224
[39] Hohl A, van der Linden H J C, Roy R, Goldsztein G, Broner F, and Strogatz S H 1995 Phys. Rev. Lett. 74 2220
[40] Kim Y H and Kim J J 1997 Phys. Rev. B 55 R11933
[41] Suen J S and Erskine J L 1997 Phys. Rev. Lett. 78 3567
[42] Chakrabarti B K and Acharyya M 1999 Rev. Mod. Phys. 71 847
[43] Lee W Y, Choi B C, Lee J, Yao C C, Xu Y B, Hasko D G, and Bland J A C 1999 Appl. Phys. Lett. 74 1609
[44] Lee W, Kim J H, Hwang J G, Noh H R, and Jhe W 2016 Phys. Rev. E 94 032141
[45] Zhong F, Zhang J X, and Siu G G 1994 J. Phys.: Condens. Matter 6 7785
[46] Zhong F and Zhang J X 1995 Phys. Rev. E 51 2898
[47] Zhong F, Zhang J X, and Liu X 1995 Phys. Rev. E 52 1399
[48] Zhong F and Zhang J X 1995 Phys. Rev. Lett. 75 2027
[49] Zhang J X, Zhong F, and Siu G G 1996 Solid State Commun. 97 847
[50] Zhong F, Dong J M, and Xing D Y 1998 Phys. Rev. Lett. 80 1118
[51] Zhong F 2002 Phys. Rev. B 66 060401
[52] Yıldız S, Pekcan Ö, Berker A N, and Özbek H 2004 Phys. Rev. E 69 031705
[53] Zhong F and Chen Q Z 2005 Phys. Rev. Lett. 95 175701
[54] Zhong F 2017 Front. Phys. 12 126402
[55] Zhong F 2012 Phys. Rev. E 86 022104
[56] Fan S and Zhong F 2011 J. Stat. Phys. 143 1136
[57] Li Y T and Zhong F 2011 arXiv:1111.1573 [cond-mat.stat-mech]
[58] Pelissetto A and Vicari E 2017 Phys. Rev. Lett. 118 030602
[59] Liang N and Zhong F 2017 Phys. Rev. E 95 032124
[60] Liang N and Zhong F 2017 Front. Phys. 12 126403
[61] Bar T, Choudhary S K, Ashraf M A, Sujith K S, Puri S, Raj S, and Bansal B 2018 Phys. Rev. Lett. 121 045701
[62] Qiu L Y, Liang H Y, Yang Y B, Yang H X, Tian T, Xu Y, and Duan L M 2020 Sci. Adv. 6 eaba7292
[63] Kundu S, Patel R K, Middey S, and Bansal B 2023 Phys. Rev. E 108 024101
[64] Sides S W, Rikvold P A, and Novotny M A 1998 Phys. Rev. E 57 6512
[65] Gong S, Zhong F, Huang X, and Fan S 2010 New J. Phys. 12 043036
[66] Zhong F 2011 Applications of Monte Carlo Method in Science and Engineering ed Mordechai S (Rijeka: Intech) pp 469–493
[67] Huang Y, Yin S, Feng B, and Zhong F 2014 Phys. Rev. B 90 134108
[68] Yuan W, Yin S, and Zhong F 2021 Chin. Phys. Lett. 38 026401
[69]We solve Eq. (2) by direct Euler discretization. The time step is 0.001 for the small rates but 0.000 5 for large ones, both having been checked to bring stable results. The average is over 10 000 (for the large rates) to 20 000 samples in the presence of the noise. The initial $H$ values are chosen to be sufficiently far away from the transition region so that any initial $\phi < 0$ can rapidly equilibrate to the metastable state. The same discretization is also applied to solve Eq. (7) later. The space step is fixed to 1, while the time step is 0.01, again checked to be sufficient. The lattice is $240\times240$ and $480\times480$ with periodic boundary conditions. They results in curves with only negligible difference. More than 5 000 to 10 000 samples are employed for average.
[70] Hänggi P, Talkner P, and Borkovec M 1990 Rev. Mod. Phys. 62 251
[71] Hohenberg P C and Halperin B I 1977 Rev. Mod. Phys. 49 435
[72]We have not considered the spatial correlation of the noise. Otherwise $[\sigma]$ is smaller by $d$ and is different from $2[\zeta]$. The resultant $[\sigma]$ has also been tested to lead to a large dynamic exponent and poorer curve collapses.
[73] Zeng S L, Szeto S P, and Zhong F 2022 Phys. Scr. 97 125002
[74] Cardy J L 1985 Phys. Rev. Lett. 54 1354
[75] Fisher M E 1978 Phys. Rev. Lett. 40 1610
[76] An X, Mesterházy D, and Stephanov M A 2018 J. Stat. Mech.: Theory Exp. 2018 033207
[77] Wegner F J 1972 Phys. Rev. B 5 4529
Viewed
Full text


Abstract