arXiv subjects

Oliver Schnetz

Publications and source records attributed to Oliver Schnetz.

45 records · Page 3Linked to original sources

arXiv2005

Full Phase Diagram of the Massive Gross-Neveu Model

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.

hep-th↗

arXiv2005

The phase diagram of the massive Gross-Neveu model, revisited

The massive Gross-Neveu model is solved in the large N limit at finite temperature and chemical potential. The phase diagram features a kink-antikink crystal phase which was missed in previous works. Translated into the framework of condensed matter physics our results generalize the bipolaron lattice in non-degenerate conducting polymers to finite temperature.

hep-th↗

arXiv2005

Phase Diagram of the Gross-Neveu Model: Exact Results and Condensed Matter Precursors

Recently the revised phase diagram of the (large N) Gross-Neveu model in 1+1 dimensions with discrete chiral symmetry has been determined numerically. It features three phases, a massless and a massive Fermi gas and a kink-antikink crystal. Here we investigate the phase diagram by analytical means, mapping the Dirac-Hartree-Fock equation onto the non-relativistic Schroedinger equation with the (single gap) Lame potential. It is pointed out that mathematically identical phase diagrams appeared in the condensed matter literature some time ago in the context of the Peierls-Froehlich model and ferromagnetic superconductors.

hep-th↗

arXiv2005

On the mean-field spherical model

Exact solutions are obtained for the mean-field spherical model, with or without an external magnetic field, for any finite or infinite number N of degrees of freedom, both in the microcanonical and in the canonical ensemble. The canonical result allows for an exact discussion of the loci of the Fisher zeros of the canonical partition function. The microcanonical entropy is found to be nonanalytic for arbitrary finite N. The mean-field spherical model of finite size N is shown to be equivalent to a mixed isovector/isotensor sigma-model on a lattice of two sites. Partial equivalence of statistical ensembles is observed for the mean-field spherical model in the thermodynamic limit. A discussion of the topology of certain state space submanifolds yields insights into the relation of these topological quantities to the thermodynamic behavior of the system in the presence of ensemble nonequivalence.

cond-mat.stat-mech↗

arXiv1999

Calculation of the phi^4 6-loop non-zeta transcendental

We present an analytic calculation of the first transcendental in phi^4-Theory that is not of the form zeta(2n+1). It is encountered at 6 loops and known to be a weight 8 double sum. Here it is obtained by reducing multiple zeta values of depth <= 4. We give a closed expression in terms of a zeta-related sum for a family of diagrams that entails a class of physical graphs. We confirm that this class produces multiple zeta values of weights equal to the crossing numbers of the related knots.

hep-th↗

arXiv1998

Generating Functions for Multi-j-Symbols

A formula is derived that provides generating functions for any multi-j-symbol, such as the 3-j-symbol, the 6-j-symbol, the 9-j-symbol, etc. The result is completely determined by geometrical objects (loops and curves) in the graph of the the multi-j-symbol. A geometric-combinatorical interpretation for multi-j-symbols is given.

math-ph↗

arXiv1996

Harmonic analysis of random number generators and multiplicative groups of residue class rings

The spectral test of random number generators (R.R. Coveyou and R.D. McPherson, 1967) is generalized. The sequence of random numbers is analyzed explicitly not just via their n-tupel distributions. The generalized analysis of many generators becomes possible due to a theorem on the harmonic analysis of multiplicative groups of residue class rings. We find that the mixed multiplicative generator with power of two modulus does not pass the extended test with an ideal result. Best qualities has a new generator with the recursion formula X(k+1)=a*X(k)+c*int(k/2) mod 2^d. We discuss the choice of the parameters a, c for very large moduli 2^d and present an implementation of the suggested generator with d=256, a=2^128+2^64+2^32+62181, c=(2^160+1)*11463.

physics.comp-ph↗

arXiv1996

Harmonic analysis of random number generators

The spectral test of random number generators (R.R. Coveyou and R.D. McPherson, 1967) is generalized. The sequence of random numbers is analyzed explicitly, not just via their n-tupel distributions. We find that the mixed multiplicative generator with power of two modulus does not pass the extended test with an ideal result. Best qualities has a new generator with the recursion formula X(k+1)=a*X(k)+c*int(k/2) mod 2^d. We discuss the choice of the parameters a, c for very large moduli 2^d and present an implementation of the suggested generator with d=256, a=2^128+2^64+2^32+62181, c=(2^160+1)*11463.

physics.comp-ph↗

arXiv1996

Natural renormalization

A careful analysis of differential renormalization shows that a distinguished choice of renormalization constants allows for a mathematically more fundamental interpretation of the scheme. With this set of a priori fixed integration constants differential renormalization is most closely related to the theory of generalized functions. The special properties of this scheme are illustrated by application to the toy example of a free massive bosonic theory. Then we apply the scheme to the phi^4-theory. The two-point function is calculated up to five loops. The renormalization group is analyzed, the beta-function and the anomalous dimension are calculated up to fourth and fifth order, respectively.

hep-th↗