scholarly journals Precise Phase Structure in Four-fermion Interaction Model on Torus

2021 ◽  
Author(s):  
Tomohiro Inagaki ◽  
Yamato Matsuo ◽  
Hiromu Shimoji
Keyword(s):  
Phase Structure ◽  
Chemical Potential ◽  
Chiral Symmetry Breaking ◽  
Finite Size ◽  
Interaction Model ◽  
Particle Number Density ◽  
Finite Size Effect ◽  
Imaginary Time ◽  
Spatial Direction ◽  
Time Formalism

Abstract We investigate finite-size effects on chiral symmetry breaking in a four-fermion interaction model at a finite temperature and a chemical potential. Applying the imaginary time formalism, the thermal quantum field theory is constructed on an S1 in the imaginary time direction. In this paper, the finite-size effect is introduced by a compact S1 spatial direction with a U(1)-valued boundary condition. Thus, we study the model on a $\mathbb {R}^{D-2} \times S^{1} \times S^{1}$ torus. Phase diagrams are obtained by evaluating the local minima of the effective potential in the leading order of the 1/N expansion. From the grand potential, we calculate the particle number density and the pressure, then we illustrate the correspondence with the phase structure. We obtain a stable size for which the sign of the pressure flips from negative to positive as the size decreases. Furthermore, the finite chemical potential expands the parameter range that the stable size exists.

scholarly journals Four-Fermion Interaction Model on ℳD−1 ⊗ S1

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 451 ◽  
Author(s):  
Tomohiro Inagaki ◽  
Yamato Matsuo ◽  
Hiromu Shimoji
Keyword(s):  
Chiral Symmetry ◽  
Effective Potential ◽  
Casimir Force ◽  
Chiral Symmetry Breaking ◽  
Finite Size ◽  
Interaction Model ◽  
Finite Size Effect ◽  
Leading Order ◽  
Fermion Fields ◽  
Critical Lines

Four-fermion interaction models are often used as simplified models of interacting fermion fields with the chiral symmetry. The chiral symmetry is dynamically broken for a larger four-fermion coupling. It is expected that the broken symmetry is restored under extreme conditions. In this paper, the finite size effect on the chiral symmetry breaking is investigated in the four-fermion interaction model. We consider the model on a flat spacetime with a compactified spatial coordinate, M D − 1 ⊗ S 1 and obtain explicit expressions of the effective potential for arbitrary spacetime dimensions in the leading order of the 1 / N expansion. Evaluating the effective potential, we show the critical lines which divide the symmetric and the broken phase and the sign-flip condition for the Casimir force.

PHASE STRUCTURE OF QED3 AT FINITE CHEMICAL POTENTIAL AND TEMPERATURE

2007 ◽  
Vol 22 (06) ◽  
pp. 449-456 ◽  
Author(s):  
MIN HE ◽  
HONG-TAO FENG ◽  
WEI-MIN SUN ◽  
HONG-SHI ZONG
Keyword(s):  
Phase Diagram ◽  
Wave Function ◽  
Symmetry Breaking ◽  
Quantum Electrodynamics ◽  
Phase Structure ◽  
Chemical Potential ◽  
Chiral Symmetry Breaking ◽  
Three Dimensional ◽  
Mass Function ◽  
Wave Function Renormalization

We study the dynamical chiral symmetry breaking (DCSB) of three-dimensional quantum electrodynamics (QED3) at finite chemical potential and temperature in the framework of Dyson–Schwinger approach. Based on the rainbow approximation and assumption that the wave-function renormalization factor equals to one, the dynamically generated mass function is derived and then the corresponding phase diagram in the (T, μ) plane is obtained.

scholarly journals PHASE STRUCTURE OF A FOUR- AND EIGHT-FERMION INTERACTION MODEL AT FINITE TEMPERATURE AND CHEMICAL POTENTIAL IN ARBITRARY DIMENSIONS

2010 ◽  
Vol 25 (25) ◽  
pp. 4757-4774 ◽  
Author(s):  
MASAKO HAYASHI ◽  
TOMOHIRO INAGAKI ◽  
WATARU SAKAMOTO
Keyword(s):  
Finite Temperature ◽  
Phase Structure ◽  
Chemical Potential ◽  
Interaction Model ◽  
Leading Order ◽  
First Order ◽  
First Order Phase Transition ◽  
Arbitrary Space ◽  
Arbitrary Dimensions ◽  
First Order Phase

The phase structure of a four- and eight-fermion interaction model is investigated at finite temperature and chemical potential in arbitrary space–time dimensions, 2 ≤ D < 4. The effective potential and the gap equation are calculated in the leading order of the 1/N expansion. If the first order phase transition takes place, the phase boundary dividing the symmetric and the broken phase is modified by the eight-fermion interaction.

scholarly journals Size Effect in Grand-canonical Monte-Carlo Simulation of Solutions of Electrolyte

2019 ◽  
Vol 35 (2) ◽  
Author(s):  
Nguyen Viet Duc
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Size Effect ◽  
Chemical Potential ◽  
Finite Size ◽  
Simulation Method ◽  
Electrolyte Solutions ◽  
Finite Size Effect ◽  
Grand Canonical Monte Carlo ◽  
Grand Canonical

Abstract: A Grand-canonical Monte-Carlo simulation method is investigated. Due to charge neutrality requirement of electrolyte solutions, ions must be added to or removed from the system in groups. It is then implemented to simulate solution of 1:1, 2:1 and 2:2 salts at different concentrations using the primitive ion model. We investigate how the finite size of the simulation box can influence statistical quantities of the salt system. Remarkably, the method works well down to a system as small as one salt molecule. Although the fluctuation in the statistical quantities increases as the system gets smaller, their average values remain equal to their bulk value within the uncertainty error. Based on this knowledge, the osmotic pressures of the electrolyte solutions are calculated and shown to depend linearly on the salt concentrations within the concentration range simulated. Chemical potential of ionic salt that can be used for simulation of these salts in more complex system are calculated. Keywords: GCMC, electrolyte solution simulation, primitive ion model, finite size effect.

scholarly journals Horizon radiation reaction forces

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Walter D. Goldberger ◽  
Ira Z. Rothstein
Keyword(s):  
Black Hole ◽  
Equations Of Motion ◽  
Finite Size ◽  
Radiation Reaction ◽  
Effective Field ◽  
Compact Objects ◽  
Finite Size Effect ◽  
Binary Black Holes ◽  
Dissipative Effects ◽  
Reaction Forces

Abstract Using Effective Field Theory (EFT) methods, we compute the effects of horizon dissipation on the gravitational interactions of relativistic binary black hole systems. We assume that the dynamics is perturbative, i.e it admits an expansion in powers of Newton’s constant (post-Minkowskian, or PM, approximation). As applications, we compute corrections to the scattering angle in a black hole collision due to dissipative effects to leading PM order, as well as the post-Newtonian (PN) corrections to the equations of motion of binary black holes in non-relativistic orbits, which represents the leading order finite size effect in the equations of motion. The methods developed here are also applicable to the case of more general compact objects, eg. neutron stars, where the magnitude of the dissipative effects depends on non-gravitational physics (e.g, the equation of state for nuclear matter).

On The Phase Structure of the Asymmetric Three-State Potts Model

1982 ◽  
Vol 21 ◽  
Author(s):  
G. v. Gehlen
Keyword(s):  
Phase Boundary ◽  
Potts Model ◽  
Phase Structure ◽  
Asymmetry Parameter ◽  
Finite Size ◽  
Critical Index ◽  
Incommensurate Phase ◽  
Finite Size Scaling ◽  
Lifshitz Point ◽  
The Asymmetry

ABSTRACTFinite-size scaling is applied to the Hamiltonian version of the asymmetric Z3-Potts model. Results for the phase boundary of the commensurate region and for the corresponding critical index ν are presented. It is argued that there is no Lifshitz point, the incommensurate phase extending down to small values of the asymmetry parameter.

scholarly journals Theoretical Investigation of the Size Effect on the Oxygen Adsorption Energy of Coinage Metal Nanoparticles

2021 ◽  
Author(s):  
Amir H. Hakimioun ◽  
Elisabeth M. Dietze ◽  
Bart D. Vandegehuchte ◽  
Daniel Curulla-Ferre ◽  
Lennart Joos ◽  
...  
Keyword(s):  
Particle Size ◽  
Size Effect ◽  
Adsorption Energy ◽  
Single Point ◽  
Finite Size ◽  
Geometry Optimization ◽  
Oxygen Adsorption ◽  
Finite Size Effect ◽  
Full Geometry Optimization ◽  
Coinage Metal

AbstractThis study evaluates the finite size effect on the oxygen adsorption energy of coinage metal (Cu, Ag and Au) cuboctahedral nanoparticles in the size range of 13 to 1415 atoms (0.7–3.5 nm in diameter). Trends in particle size effects are well described with single point calculations, in which the metal atoms are frozen in their bulk position and the oxygen atom is added in a location determined from periodic surface calculations. This is shown explicitly for Cu nanoparticles, for which full geometry optimization only leads to a constant offset between relaxed and unrelaxed adsorption energies that is independent of particle size. With increasing cluster size, the adsorption energy converges systematically to the limit of the (211) extended surface. The 55-atomic cluster is an outlier for all of the coinage metals and all three materials show similar behavior with respect to particle size. Graphic Abstract

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