Liquidgas phase transitions and $\mathcal{C}\mathcal{K}$ symmetry in quantum field theories
A general fieldtheoretic framework for the treatment of liquidgas phase transitions is developed. Starting from a fundamental fourdimensional field theory at nonzero temperature and density, an effective threedimensional field theory is derived. The effective field theory has a sign problem at finite density. Although finite density explicitly breaks charge conjugation C , there remains a symmetry under C K , where K is complex conjugation. Here, we consider four models: relativistic fermions, nonrelativistic fermions, static fermions and classical particles. The interactions are via an attractive potential due to scalar field exchange and a repulsive potential due to massive vector exchange. The fieldtheoretic representation of the partition function is closely related to the equivalence of the sineGordon field theory with a classical gas. The thermodynamic behavior is extracted from C K symmetric complex saddle points of the effective field theory at tree level. In the cases of nonrelativistic fermions and classical particles, we find complex saddle point solutions but no firstorder transitions, and neither model has a ground state at tree level. The relativistic and static fermions show a liquidgas transition at tree level in the effective field theory. The liquidgas transition, when it occurs, manifests as a firstorder line atmore »
 Authors:

^{[1]};
^{[2]};
^{[2]}
 Brookhaven National Lab. (BNL), Upton, NY (United States). RIKEN Research Center
 Washington Univ., St. Louis, MO (United States). Dept. of Physics
 Publication Date:
 Report Number(s):
 BNL1141662017JA
Journal ID: ISSN 24700010; PRVDAQ; R&D Project: PO3
 Grant/Contract Number:
 SC00112704
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 95; Journal Issue: 7; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Research Org:
 Brookhaven National Lab. (BNL), Upton, NY (United States). RIKEN Research Center
 Sponsoring Org:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Riken BNL Research Center
 OSTI Identifier:
 1377048
Nishimura, Hiromichi, Ogilvie, Michael C., and Pangeni, Kamal. Liquidgas phase transitions and CK symmetry in quantum field theories. United States: N. p.,
Web. doi:10.1103/PhysRevD.95.076003.
Nishimura, Hiromichi, Ogilvie, Michael C., & Pangeni, Kamal. Liquidgas phase transitions and CK symmetry in quantum field theories. United States. doi:10.1103/PhysRevD.95.076003.
Nishimura, Hiromichi, Ogilvie, Michael C., and Pangeni, Kamal. 2017.
"Liquidgas phase transitions and CK symmetry in quantum field theories". United States.
doi:10.1103/PhysRevD.95.076003. https://www.osti.gov/servlets/purl/1377048.
@article{osti_1377048,
title = {Liquidgas phase transitions and CK symmetry in quantum field theories},
author = {Nishimura, Hiromichi and Ogilvie, Michael C. and Pangeni, Kamal},
abstractNote = {A general fieldtheoretic framework for the treatment of liquidgas phase transitions is developed. Starting from a fundamental fourdimensional field theory at nonzero temperature and density, an effective threedimensional field theory is derived. The effective field theory has a sign problem at finite density. Although finite density explicitly breaks charge conjugation C , there remains a symmetry under C K , where K is complex conjugation. Here, we consider four models: relativistic fermions, nonrelativistic fermions, static fermions and classical particles. The interactions are via an attractive potential due to scalar field exchange and a repulsive potential due to massive vector exchange. The fieldtheoretic representation of the partition function is closely related to the equivalence of the sineGordon field theory with a classical gas. The thermodynamic behavior is extracted from C K symmetric complex saddle points of the effective field theory at tree level. In the cases of nonrelativistic fermions and classical particles, we find complex saddle point solutions but no firstorder transitions, and neither model has a ground state at tree level. The relativistic and static fermions show a liquidgas transition at tree level in the effective field theory. The liquidgas transition, when it occurs, manifests as a firstorder line at low temperature and high density, terminated by a critical end point. The mass matrix controlling the behavior of correlation functions is obtained from fluctuations around the saddle points. Due to the C K symmetry of the models, the eigenvalues of the mass matrix are not always real but can be complex. This then leads to the existence of disorder lines, which mark the boundaries where the eigenvalues go from purely real to complex. The regions where the mass matrix eigenvalues are complex are associated with the critical line. In the case of static fermions, a powerful duality between particles and holes allows for the analytic determination of both the critical line and the disorder lines. Depending on the values of the parameters, either zero, one, or two disorder lines are found. Our numerical results for relativistic fermions give a very similar picture.},
doi = {10.1103/PhysRevD.95.076003},
journal = {Physical Review D},
number = 7,
volume = 95,
place = {United States},
year = {2017},
month = {4}
}