Revised phase diagram of the Gross-Neveu model

Thies, Michael; Urlichs, Konrad

doi:10.1103/physrevd.67.125015

Cited by 91 publications

(237 citation statements)

References 18 publications

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“…Incidentally, we should like to point out that all the fat lines in Fig. 3 representing the boundaries of the sheets I, II have been taken from sources independent of the present work [15,17,19]. The fact that the computed surfaces connect very accurately constitutes a test for our algebraic and numerical calculations.…”

Section: ) Crystal Phase and The Revised Phase Diagrammentioning

confidence: 92%

“…This issue was addressed by Barducci et al in 1995 [15] (for earlier, partial results, see also [16]). Recent findings about the massless GN model [17,18,19] cast doubts on the full validity of their calculations. The assumption that the scalar condensate is spatially homogeneous is apparently too restrictive and misses important physics related to the existence of kink-antikink baryons.…”

Section: Introductionmentioning

confidence: 99%

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Full phase diagram of the massive Gross–Neveu model

2006

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The massive Gross-Neveu model is solved in the large N limit at finite temperature and chemical potential. The scalar potential is given in terms of Jacobi elliptic functions. It contains three parameters which are determined by transcendental equations. Self-consistency of the scalar potential is proved. The phase diagram for non-zero bare quark mass is found to contain a kink-antikink crystal phase as well as a massive fermion gas phase featuring a cross-over from light to heavy effective fermion mass. For zero bare quark mass we recover the three known phases kink-antikink crystal, massless fermion gas, and massive fermion gas. All phase transitions are shown to be of second order. Equations for the phase boundaries are given and solved numerically. Implications on condensed matter physics are indicated where our results generalize the bipolaron lattice in non-degenerate conducting polymers to finite temperature.

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Section: ) Crystal Phase and The Revised Phase Diagrammentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Full phase diagram of the massive Gross–Neveu model

2006

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“…To see what happens at imaginary µ, it is again advantageous to switch to the Casimir interpretation: T, µ are mapped onto the size L and the boundary phase θ, and there is no known mechanism which would induce a breakdown of translational invariance as a function of these parameters in a quantum phase transition. To further test this intuitive expectation, we have [21,22]. The critical line AB is the same as in Fig.…”

Section: Kink-antikink Crystal From Imaginary Chemical Potential?mentioning

confidence: 97%

“…5 have been derived under the assumption that the order parameter ψ ψ is constant in space, i.e., the mean field acts like a mass term. Actually, at real chemical potential, an inhomogeneous phase with a periodically modulated scalar condensate, a kink-antikink crystal, is more stable in some part of the (µ, T )-plane [21,22]. The phase diagram of the GN model including the crystal phase is shown in Fig.…”

Section: Kink-antikink Crystal From Imaginary Chemical Potential?mentioning

confidence: 99%

How to get from imaginary to real chemical potential

Karbstein

Thies

2007

Phys. Rev. D

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Using the exactly solvable Gross-Neveu model as theoretical laboratory, we analyse in detail the relationship between a relativistic quantum field theory at real and imaginary chemical potential. We find that one can retrieve the full information about the phase diagram of the theory from an imaginary chemical potential calculation. The prerequisite is to evaluate and analytically continue the effective potential for the chiral order parameter, rather than thermodynamic observables or phase boundaries. In the case of an inhomogeneous phase, one needs to compute the full effective action, a functional of the space-dependent order parameter, at imaginary chemical potential.

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“…Due to Thies and Urlichs, the phase diagram is analytically known in the limit of many flavours N [15]. This model therefore provides for a benchmark test for any new numerical method which tries to extend its reach to very dense fermionic systems.…”

Section: Setup Of the Modelmentioning

confidence: 99%

Worldline Approach to Chiral Fermions

Langfeld¹

2008

Proceedings of the XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007)

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We propose to apply "worldline numerics" to a numerical calculation of quark determinants. The Gross-Neveu model with a U(1) chiral symmetry is considered as a first test. The worldline approach allows for an analytic renormalisation, and only finite parts of the determinant require a numerical calculation. It is shown that the discretisation of the worldlines, which is central to the numerical treatment, preserves chiral symmetry exactly. Numerical results for a kink configuration as a scalar background field are shown and compared with analytical results. The case of finite fermion chemical potential is also briefly discussed.

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Revised phase diagram of the Gross-Neveu model

Cited by 91 publications

References 18 publications

Full phase diagram of the massive Gross–Neveu model

Full phase diagram of the massive Gross–Neveu model

How to get from imaginary to real chemical potential

Worldline Approach to Chiral Fermions

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