The phase diagrams of the schwinger and gross-neveu models with Wilson fermions

Kenna, Ralph; Pinto, Carlos; Sexton, James

doi:10.1016/s0920-5632(00)91770-5

Cited by 2 publications

(6 citation statements)

References 11 publications

(4 reference statements)

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“…These values comply with standard boundary requirements for Grassmann variables, namely that they are periodic in the spatial (1-) direction and antiperiodic in the temporal (2-) one [24]. The complex hopping-parameter zeroes are easily and exactly extracted from the multiplicative expression for the partition function (see [15]) and the zeroes for a system of size L = 50 are depicted in Fig. 10 in the complex 1/2κ plane.…”

Section: Wilson Fermionsmentioning

confidence: 63%

“…Departures from such smooth linear sets of zeroes were first observed for models on hierarchical and anisotropic two-dimensional lattices, for which there can exist a twodimensional distribution (area) of zeroes [10,11,12]. Since then, a host of systems have been discovered with this feature [13,14,15,16]. A common characteristic of all such two-dimensional distributions of zeroes is that the only physically relevant point at which they cross the real axis, in the thermodynamic limit, is that which corresponds to the phase transition.…”

Section: General Distribution Of Zeroesmentioning

confidence: 98%

“…Since then, a host of systems have been discovered with this feature [13,14,15,16]. A common characteristic of all such two-dimensional distributions of zeroes is that the only physically relevant point at which they cross the real axis, in the thermodynamic limit, is that which corresponds to the phase transition.…”

Section: General Distribution Of Zeroesmentioning

confidence: 99%

“…The error assigned to each point now becomes 15) having chosen σ arb to be unity. Moreover, the actual errors associated with the parameters a i are (with σ arb = 1)…”

Section: General Distribution Of Zeroesmentioning

confidence: 99%

“…3. A threeparameter fit to (2.6) for the first 8 zeroes for lattices of size L = 40, 60, 80, 100, 120, and 140 gives a 3 = 0.000002 (15), indicating the presence of a transition. With a 3 set to zero, a two-parameter fit then yields a 2 = 2.016(32), close to the expected value of 2 (which corresponds to α = 0).…”

Section: Square Lattice Ising Model With Anisotropic Couplingsmentioning

confidence: 99%

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Phase transition strength through densities of general distributions of zeroes

2004

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A recently developed technique for the determination of the density of partition function zeroes using data coming from finite-size systems is extended to deal with cases where the zeroes are not restricted to a curve in the complex plane and/or come in degenerate sets. The efficacy of the approach is demonstrated by application to a number of models for which these features are manifest and the zeroes are readily calculable.

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Section: Wilson Fermionsmentioning

confidence: 63%

Section: General Distribution Of Zeroesmentioning

confidence: 98%

Section: General Distribution Of Zeroesmentioning

confidence: 99%

“…The error assigned to each point now becomes 15) having chosen σ arb to be unity. Moreover, the actual errors associated with the parameters a i are (with σ arb = 1)…”

Section: General Distribution Of Zeroesmentioning

confidence: 99%

Section: Square Lattice Ising Model With Anisotropic Couplingsmentioning

confidence: 99%

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Phase transition strength through densities of general distributions of zeroes

2004

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Anomalous Fisher-like zeros for the canonical partition function of noninteracting fermions

Bhaduri

MacDonald²,

Dijk³

2011

EPL

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Noninteracting fermions, placed in a system with a continuous density of states, may have zeros in the N -fermion canonical partition function on the positive real β axis (or very close to it), even for a small number of particles. This results in a singular free energy, and instability in other thermal properties of the system. In the context of trapped fermions in a harmonic oscillator, these zeros are shown to be unphysical. Our results are also applicable to mean-field canonical calculations for fermions. By contrast, similar bosonic calculations with continuous density of states yield sensible results.Long back, Lee and Yang [1,2] pointed out that the onset of a phase transition could be deduced by studying the zeros of the grand partition function on the complex fugacity plane. As the number of particles goes to infinity in the thermodynamic limit, the complex zeros tend to pinch the real fugacity axis, signalling a phase transition. Later, Fisher [3] found a similar behaviour of the canonical partition function Z N (β) on the complex β (inverse temperature) plane near a phase transition. Given a single-particle partition function Z 1 (β), Z N (β) may be calculated exactly for noninteracting bosons or fermions using recursion relations [4]. The single-particle partition function may arise from a one-body trapping potential, or may be the result of a calculation in a many-body problem. In this context, Mülken et al. [5] have studied the pattern of Fisher zeros for trapped noninteracting bosons in a harmonic oscillator. As the number of bosons was increased, the real positive β axis tended to be pinched at T = T c , the Bose-Einstein condensation temperature for spatial dimensions d > 1. The behaviour of the heat capacity as a function of T also showed a sharp peak for large N at T = T c . As expected, this was found both for the exact single-particle density of states of a harmonic oscillator (HO), and for the corresponding (asymptotic) continuous density of states. Mülken et al.[5] examined the distribution of zeros on the complex β plane to classify the order of the phase transition in finite systems. Similar analyses were done with the Fisher zeros in interacting statistical models by Janke et al. [6,7].Noninteracting fermions trapped in a HO have not been studied in this context, presumably because no irregularity or phase transition is expected. However, a classical version of this formalism has been applied in a model for the thermodynamic properties of nuclear multifragmentation in heavy-ion collisions [8]. In this paper, we are especially interested in the effects of the Fermi statistics on the analytical properties of the canonical partition function. In particular, we compare results obtained from the exact single-particle partition function from the discrete HO energy spectrum, with those obtained using a continuous density of states approximation. The latter is widely used in the grand canonical formalism. With the exact HO density of states, the fermionic system shows no evidence of any phase tr...

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The phase diagrams of the schwinger and gross-neveu models with Wilson fermions

Cited by 2 publications

References 11 publications

Phase transition strength through densities of general distributions of zeroes

Phase transition strength through densities of general distributions of zeroes

Anomalous Fisher-like zeros for the canonical partition function of noninteracting fermions

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