Exploring percolation phase transition in the three-dimensional Ising model with machine learning

[1]
M. A. Stephanov, K. Rajagopal, and E. V. Shuryak, Phys. Rev. Lett. 81, 4816 (1998)
[2]
J. Adams, et al., Nucl. Phys. A 757, 102 (2005)
[3]
M. Asakawa, U. W. Heinz, and B. Muller, Phys. Rev. Lett. 85, 2072 (2000)
[4]
V. Koch, A. Majumder and J. Randrup, Phys. Rev. Lett. 95, 182301 (2005)
[5]
Y. Aoki, G. Endrodi, Z. Fodor, et al., Nature 443, 675 (2006)
[6]
M. Asakawa and K. Yazaki, Nucl. Phys. A 504, 668 (1989)
[7]
E. S. Bowman, J. I. Kapusta, Phys. Rev. C 79, 015202 (2009)
[8]
Z. Fodor and S. D. Katz, JHEP 2004, 50 (2004)
[9]
R. V. Gavai and S. Gupta, Phys. Rev. D 78, 114503 (2008)
[10]
J. N. Guenther, Eur. Phys. J. A 57, 136 (2021)
[11]
A. Bazavov, et al., Phys. Rev. D 90, 094503 (2014)
[12]
X. Li, R. Guo, Y. Zhou, et al., Chin. Phys. C 47(3), 034101 (2023)
[13]
X. Li, M. Xu, Y. Zhang, et al., Phys. Rev. C 105, 064904 (2022)
[14]
L. Chen, Y. Y. Zhao, X. Li, et al., Int. J. Mod. Phys. E 30, 2150056 (2021)
[15]
X. Pan, L. Chen, X. S. Chen, et al., Nucl. Phys. A 913, 206 (2013)
[16]
X. Li, Y. Zhong, R. Guo, et al., arXiv: 2305.18468
[17]
R. D. Pisarski and F. Wilczek, Phys. Rev. D 29, 338 (1984)
[18]
M. Asakawa, J. Phys. G: Nucl. Part. Phys. 36, 064042 (2009)
[19]
P. de Forcrand and O. Philipsen, Phys. Rev. Lett. 105, 152001 (2010)
[20]
F. Karsch, E. Laermann and C. Schmidt, Phys. Lett. B 520, 41 (2001)
[21]
M. A. Stephanov, Phys. Rev. Lett. 107, 052301 (2011)
[22]
P. Parotto, Parametrized Equation of State for QCD from 3D Ising Model, PoS CPOD2017, 036 (2018)
[23]
A. Carollo, D. Valenti and B. Spagnolo, Phys. Rep. 838, 1 (2020)
[24]
M. Gori, R. Franzosi, G. Pettini, et al., J. Phys. A: Math. Theor. 55, 375002 (2022)
[25]
S. Sachdev, Quantum Phase Transitions, Second edition (Cambridge, England: Cambridge University Press, 2011), p. 306
[26]
K. Binder and P. Virnau, J. Chem. Phys. 145, 211701 (2016)
[27]
K. Binder, J. Phys. A: Math. Theor. 50, 061001 (2017)
[28]
M. Grady, J. Phys.: Condens. Matter 35, 285401 (2023)
[29]
A. A. Saberi and H. Dashti-Naserabadi, EPL 92, 67005 (2010)
[30]
B. K. Srivastava, Nucl. Phys. A 926, 142 (2014)
[31]
R. P. Scharenberg, B. K. Srivastava and C. Pajares, Phys. Rev. D 100, 114040 (2019)
[32]
K. Goswami, D. Sahu and R. Sahoo, Phys. Rev. D 107, 014003 (2023)
[33]
S. Fortunato, J. Phys. A 36, 4269 (2003)
[34]
S. Fortunato, F. Karsch, P. Petreczky, et al., Nucl. Phys. B (Proc. Suppl.) 94, 398 (2001)
[35]
S. Fortunato, H. Satz, Phys. Lett. B 475, 311 (2000)
[36]
C. Gattringer, Phys. Lett. B 690, 179 (2010)
[37]
J. Danzer, C. Gattringer, S. Borsanyi, et al., Center clusters and their percolation properties in lattice QCD, PoS Lattice2010, 176 (2010)
[38]
M. A. Braun, J. Dias de Deus, A. S. Hircsh, et al., Phys. Rep. 599, 1 (2015)
[39]
A. Coniglio, Phys. Rev. B 13, 2194 (1976)
[40]
M. Xu, M. Yu and L. Liu, Phys. Rev. Lett. 100, 092301 (2008)
[41]
A. Coniglio, C. R. Nappi, F. Peruggi, et al., Commun. Math. Phys. 51, 315 (1976)
[42]
H. Miiller-Krumbhaar, Phys. Lett. A 48, 459 (1974)
[43]
C. M. Fortuin and P. W. Kasteleyn, Physica 57, 536 (1972)
[44]
A. Coniglio and W. Klein, J. Phys. A: Math. Gen. 13, 2775 (1980)
[45]
G. E. Hinton and R. R. Salakhutdinov, Science 313, 504 (2006)
[46]
Y. L. Cun, Y. Bengio, and G. Hinton, Nature 521, 436 (2015)
[47]
P. Mehta, M. Bukov, C. H. Wang, et al., Phys. Rep. 810, 1 (2019)
[48]
G. Carleo, I. Cirac, K. Cranmer, et al., Rev. Mod. Phys. 91, 045002 (2019)
[49]
L. Wang, Phys. Rev. B 94, 195105 (2016)
[50]
S. J. Wetzel, Phys. Rev. E 96, 022140 (2017)
[51]
W. Hu, R. R. P. Singh and R. T. Scalettar, Phys. Rev. E 95, 062122 (2017)
[52]
R. Zhang, B. Wei, D. Zhang, et al., Phy. Rev. B 99, 094427 (2019)
[53]
K. Kashiwa, Y. Kikuchi and A. Tanaka, Prog. Theor. Exp. Phys. 2019, 083A (2019)
[54]
D. W. Tola and M. Bekele, Condens. Matter 8, 83 (2023)
[55]
W. Zhang, J. Liu and TC. Wei, Phys. Rev. E 99, 032142 (2019)
[56]
J. Zhang, B. Zhang, J. Xu, et al., Phys. Rev. E 105, 024144 (2022)
[57]
J. Carrasquilla and R. G. Melko, Nat. Phys. 13, 431 (2017)
[58]
E. P. L. van Nieuwenburg, Y. H. Liu and S. D. Huber, Nat. Phys. 13, 435 (2017)
[59]
P. Ponte and R. G. Melko, Phys. Rev. B 96, 205146 (2017)
[60]
A. Canabarro, F. F. Fanchini, A. L. Malvezzi, et al., Phys. Rev. B 100, 045129 (2019)
[61]
S. S. Funai, D. Giataganas, Phys. Rev. Res. 2, 033415 (2020)
[62]
G. Hu, Y. Sun, T. Liu, et al., Sci. China-Phys. Mech. Astron. 66, 120511 (2023)
[63]
V. E. Ising, Z. Physik., 31 : 253 (1925)
[64]
M. W. Berry, A. Mohamed, B. W. Yap, Supervised and unsupervised learning for data science, (Cham: Springer, 2019), p. 12
[65]
H. Abdi and L. J. Williams, WIREs. Comp. Stat. 2, 433 (2010)
[66]
F. R. S. Karl Pearson, Philosophical Magazine 2, 559 (1901)
[67]
W. Yu and P. Lyu, Physica A 559, 125065 (2020)
[68]
Y. Ganin, E. Ustinova, H. Ajakan, et al., JMLR 17, 1 (2016)
[69]
S. J. Pan and Q. Yang, IEEE Transactions on knowledge and data engineering 22, 1345 (2010)
[70]
C. Tan, F. Sun, T. Kong, et al., A survey on deep transfer learning, in Proceedings of the 27th International Conference on Artificial Neural Networks, edited by V. Kůrková, Y. Manolopoulos, B. Hammer, et al., (Cham: Springer International Publishing, 2018), p. 270
[71]
A. A. Saberi, Phys. Rep. 578, 1 (2015)
[72]
A. Pelissetto and E. Vicari, Phys. Rep. 368, 549 (2002)
[73]
F. Winter, W. Janke and A. M. J. Schakel, Phys. Rev. E 77, 061108 (2008)
[74]
A. A. Saberi, J. Stat. Mech. 2009, P07030 (2009)
[75]
A. M. Ferrenberg, J. Xu and D. P. Landu, Phys. Rev. E 97, 043301 (2018)
[76]
P. Hou, S. Fang, J. Wang, et al., Phys. Rev. E 99, 042150 (2019)
[77]
A. Conigliot, C. R. Nappi, F. Peruggi, et al., J. Phys. A: Math. Gen. 10, 205 (1977)
[78]
J. Shen, F. Liu, S. Chen, et al., Phys. Rev. E 105, 064139 (2022)
[79]
J. Shen, W. Li, S. Deng, et al., Phys. Rev. E 103, 052140 (2021)
[80]
A. R. de la Rocha, P. M. C. de Oliveira and J. J. Arenzon, Phys. Rev. E 91, 042113 (2015)
[81]
S. Fortunato, F. Karsch, P. Petreczky, et al., Nucl. Phys. Proc. Suppl. 94, 398 (2001)
[82]
Y. Tomita and Y. Okabe, J. Phys. Soc. Jpn. 71, 1570 (2002)