scholarly journals The SU(3) spin model with chemical potential by series expansion techniques

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Jangho Kim ◽  
Anh Quang Pham ◽  
Owe Philipsen ◽  
Jonas Scheunert
Keyword(s):  
Equation Of State ◽  
Strong Coupling ◽  
Chemical Potential ◽  
Spin Model ◽  
Strong Coupling Regime ◽  
Nearest Neighbour ◽  
Reasonable Accuracy ◽  
New Methods ◽  
Current Series ◽  
Sign Problem

Abstract The SU(3) spin model with chemical potential corresponds to a simplified version of QCD with static quarks in the strong coupling regime. It has been studied previously as a testing ground for new methods aiming to overcome the sign problem of lattice QCD. In this work we show that the equation of state and the phase structure of the model can be fully determined to reasonable accuracy by a linked cluster expansion. In particular, we compute the free energy to 14-th order in the nearest neighbour coupling. The resulting predictions for the equation of state and the location of the critical end points agree with numerical determinations to $$ \mathcal{O} $$ O (1%) and $$ \mathcal{O} $$ O (10%), respectively. While the accuracy for the critical couplings is still limited at the current series depth, the approach is equally applicable at zero and non-zero imaginary or real chemical potential, as well as to effective QCD Hamiltonians obtained by strong coupling and hopping expansions.

scholarly journals Strong coupling methods in QCD thermodynamics

2021 ◽  
Author(s):  
Owe Philipsen
Keyword(s):  
Monte Carlo ◽  
Strong Coupling ◽  
Chemical Potential ◽  
Yang Mills ◽  
Coupling Methods ◽  
Sign Problem ◽  
Monte Carlo Studies ◽  
Long Time ◽  
Scaling Region ◽  
Strong Coupling Expansions

AbstractFor a long time, strong coupling expansions have not been applied systematically in lattice QCD thermodynamics, in view of the success of numerical Monte Carlo studies. The persistent sign problem at finite baryo-chemical potential, however, has motivated investigations using these methods, either by themselves or combined with numerical evaluations, as a route to finite density physics. This article reviews the strategies, by which a number of qualitative insights have been attained, notably the emergence of the hadron resonance gas or the identification of the onset transition to baryon matter in specific regions of the QCD parameter space. For the simpler case of Yang–Mills theory, the deconfinement transition can be determined quantitatively even in the scaling region, showing possible prospects for continuum physics.

A model for polysomatism

1986 ◽  
Vol 50 (355) ◽  
pp. 149-156 ◽  
Author(s):  
Geoffrey D. Price ◽  
Julia Yeomans
Keyword(s):  
Magnetic Field ◽  
Chemical Potential ◽  
Spin Model ◽  
Nearest Neighbour ◽  
Key Factors ◽  
Competing Interactions ◽  
Annni Model ◽  
The Stability

AbstractWe show that the structures and phases developed in a variety of polysomatic series, including the biopyroboles, are similar to those predicted by a simple spin model—the Axial Next-Nearest-Neighbour Ising (ANNNI) model in a magnetic field. We argue that the different polysomatic structures can be considered as thermodynamically stable phases, composed of ordered sequences of chemically distinct structural modules. We suggest that the key factors which determine the stability of polysomatic phases are (a) the chemical potential, which controls the proportion of the different structural modules, and (b) the competing interactions between first and second neighbour modules within the structures.

scholarly journals Dual Formulation and Phase Diagram of Lattice QCD in the Strong Coupling Regime

2018 ◽  
Vol 175 ◽  
pp. 07047 ◽  
Author(s):  
Giuseppe Gagliardi ◽  
Jangho Kim ◽  
Wolfgang Unger
Keyword(s):  
Lattice Qcd ◽  
Strong Coupling ◽  
Strong Coupling Expansion ◽  
Strong Coupling Limit ◽  
Strong Coupling Regime ◽  
Staggered Fermions ◽  
Chiral Transition ◽  
Occupation Numbers ◽  
Sign Problem ◽  
Limiting Case

We present the computation of invariants that arise in the strong coupling expansion of lattice QCD. These invariants are needed for Monte Carlo simulations of Lattice QCD with staggered fermions in a dual, color singlet representation. This formulation is in particular useful to tame the finite density sign problem. The gauge integrals in this limiting case β → 0 are well known, but the gauge integrals needed to study the gauge corrections are more involved. We discuss a method to evaluate such integrals. The phase boundary of lattice QCD for staggered fermions in the μB – T plane has been established in the strong coupling limit. We present numerical simulations away from the strong coupling limit, taking into account the higher order gauge corrections via plaquette occupation numbers. This allows to study the nuclear and chiral transition as a function of β.

scholarly journals Chiral symmetry in SU(Nc) gauge theories at high density

2014 ◽  
Vol 29 (25) ◽  
pp. 1445004 ◽  
Author(s):  
E. T. Tomboulis
Keyword(s):  
Strong Coupling ◽  
Cluster Expansion ◽  
Gauge Theories ◽  
Chemical Potential ◽  
Gauge Coupling ◽  
Exact Result ◽  
Spontaneous Breaking ◽  
Strong Coupling Regime ◽  
Coupling Region ◽  
Lattice Gauge

SU(Nc) lattice gauge theories with Nf flavors of massless staggered fermions are studied in the presence of quark chemical potential μ. A recent exact result that in the strong coupling limit (vanishing inverse gauge coupling β) and for sufficiently large μ the theory is in a chiral symmetric phase is here extended into the finite gauge coupling region. These and similar results are obtained by means of a cluster expansion which combines a fermion spacelike hopping expansion and a strong coupling plaquette expansion. The cluster expansion is shown to converge for sufficiently large μ and small β at any temperature T. All expectations of chirally noninvariant local fermion operators vanish identically, or, equivalently, their correlations cluster exponentially within the expansion. This implies the absence of spontaneous breaking of (any part of) the global chiral symmetries in the theory. The resulting phase at low T may be described as a "quarkyonic" matter phase. There is thus absence of any superfluidity or color superconductivity in this strong coupling regime. Implications for the phase diagram of SU(Nc) theories in the region of large chemical potential are discussed.

Strong Coupling: Polariton Bose Condensation

2017 ◽  
Author(s):  
Alexey V. Kavokin ◽  
Jeremy J. Baumberg ◽  
Guillaume Malpuech ◽  
Fabrice P. Laussy
Keyword(s):  
Strong Coupling ◽  
Room Temperature ◽  
Elevated Temperatures ◽  
Dissipative System ◽  
Bose Condensation ◽  
Einstein Condensation ◽  
Strong Coupling Regime ◽  
Stimulated Scattering ◽  
Exciton Polaritons ◽  
Bose Einstein

In this Chapter we address the physics of Bose-Einstein condensation and its implications to a driven-dissipative system such as the polariton laser. We discuss the dynamics of exciton-polaritons non-resonantly pumped within a microcavity in the strong coupling regime. It is shown how the stimulated scattering of exciton-polaritons leads to formation of bosonic condensates that may be stable at elevated temperatures, including room temperature.

Strong coupling: resonant effects

2017 ◽  
Author(s):  
Alexey V. Kavokin ◽  
Jeremy J. Baumberg ◽  
Guillaume Malpuech ◽  
Fabrice P. Laussy
Keyword(s):  
Strong Coupling ◽  
Experimental Studies ◽  
Strong Coupling Regime ◽  
Theoretical Studies ◽  
Stimulated Scattering ◽  
Quantum Theories ◽  
Pump Probe ◽  
Exciton Polaritons ◽  
Linear Optical Properties ◽  
Experimental And Theoretical Studies

This chapter presents experimental studies performed on planar semiconductor microcavities in the strong-coupling regime. The first section reviews linear experiments performed in the 1990s that evidence the linear optical properties of cavity exciton-polaritons. The chapter is then focused on experimental and theoretical studies of resonantly excited microcavity emission. We mainly describe experimental configuations in which stimulated scattering was observed due to formation of a dynamical condensate of polaritons. Pump-probe and cw experiments are described in addition. Dressing of the polariton dispersion and bistability of the polariton system due to inter-condensate interactions are discussed. The semiclassical and the quantum theories of these effects are presented and their results analysed. The potential for realization of devices is also discussed.

EQUATION OF STATE OF ASYMMETRIC NUCLEAR MATTER WITH GOGNY AND COULOMB INTERACTIONS

1990 ◽  
Vol 05 (14) ◽  
pp. 1071-1080 ◽  
Author(s):  
S. W. HUANG ◽  
M. Z. FU ◽  
S. S. WU ◽  
S. D. YANG
Keyword(s):  
Equation Of State ◽  
Nuclear Matter ◽  
Coulomb Interaction ◽  
Chemical Potential ◽  
Compression Modulus ◽  
Nucleon Nucleon ◽  
Effective Density ◽  
Coulomb Interactions ◽  
Asymmetric Nuclear Matter ◽  
Nucleon Nucleon Interaction

The equation of state of the asymmetric nuclear matter is calculated with the Gogny D1 effective density-dependent nucleon-nucleon interaction and the Coulomb interaction in the framework of the finite-temperature HF method with the rearrangement term. The dependence of the thermodynamical properties such as the critical temperature of the liquid-gas phase transition, the chemical potential, the compression modulus and the entropy on the Coulomb interaction in nuclear matter is treated by using a shielded two-body Coulomb potential and this method has been found to be a reasonable and effective approach.

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