Three-dimensional Gross-Neveu model at nonzero temperature and in an external magnetic field

The phase structure of the (2+1) Gross-Neveu model at nonzero temperatureT and in an external fieldH is studied in the leading order of the 1/N expansion. It is shown that for any fixed value ofT there exists a critical valueH _c of the magnetic field such that whenH>H _c the chiral invariance of the model is spontaneously broken. For fixedH, there exists a critical value of the temperatureT _c (H) such that forT>T _c (H) the original symmetry of the model is restored. The phase portrait of the model is constructed in theH-T plane.Institute of High Energy Physics, Serpukhov. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 1, pp. 3–11, January, 1992.     

Three-dimensional Gross-Neveu model in an external magnetic field. I

Institute of High Energy Physics, Serpukhov. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 89, No. 2, pp. 211–221, November, 1991     

Cyclotomic construction of strong external difference families in finite fields

Strong external difference families (SEDFs) and their generalizations GSEDFs and BGSEDFs in a finite abelian group G are combinatorial designs introduced by Paterson and Stinson (Discret Math 339: 2891–2906, 2016) and have applications in communication theory to construct optimal strong algebraic manipulation detection codes. In this paper we firstly present some general constructions of these combinatorial designs by using difference sets and partial difference sets in G. Then, as applications of the general constructions, we construct series of SEDF, GSEDF and BGSEDF in finite fields by using cyclotomic classes. Particularly, we present an \((n,m,k,\lambda )=(243,11,22,20)\)-SEDF in \((\mathbb {F}_q,+)\ (q=3^5=243)\) by using the cyclotomic classes of order 11 in \(\mathbb {F}_q\) which answers an open problem raised in Paterson and Stinson (2016).     

Quark and gluon condensates in the Nambu-Jona-Lasinio model at finite temperature

The temperature dependence of the amplitude for decay of a scalar meson into two photons is investigated. This result is used to describe the behavior of the masses of constituent quarks, and also the behavior of the quark and gluon condensates at finite temperatures in the Nambu-Jona-Lasinio model. It is shown that the temperature dependence of all the physical quantities is determined solely by thermal variations of the divergent quark loops.Joint Institute for Nuclear Research, Dubna. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 101, No. 3, pp. 442–449, December, 1994.     

The effects of strong magnetic fields and rotation on soliton stars at finite temperature

We study the effects of strong magnetic fields and uniform rotation on the properties of soliton stars in Lee-Wick model when a temperature dependence is introduced into this model. We first recall the properties of the Lee-Wick model and study the properties of soliton solutions, in particular, the stability condition, in terms of the parameters of the model and in terms of the number of fermions N inside the soliton (for very large N) in the presence of strong magnetic fields and uniform rotation. We also calculate the effects of gravity on the stability properties of the soliton stars in the simple approximation of coupling the Newtonian gravitational field to the energy density inside the soliton, treating this as constant throughout. Following Cottingham and Vinh Mau, we also make an analysis at finite temperature and show the possibility of a phase transition which leads to a model with parameters similar to those considered by Lee and his colleagues but in the presence of magnetic fields and rotation. More specifically, the effects of magnetic fields and rotation on the soliton mass and transition temperature are computed explicitly. We finally study the evolution on these magnetized and rotating soliton stars with the temperature from the early universe to the present time.     

Supersymmetric p-branes at finite temperature

The regularized free energy of open and closed supersymmetric p-branes in (D – 1)-dimensional flat space is calculated by the method of quasiclassical quantization. The critical temperature, indicating a phase transition, is obtained. It is shown that the quantum properties of bosonic p-branes (open and closed) with p = D – 1 are identical to the properties of a massless scalar particle.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Akademii Nauk SSSR, Vol. 180, pp. 36–40, 1990.     

Zeta-function method in field theory at finite temperature

Engineering-Physics Institute, Moscow. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 78, No. 3, pp. 444–457, March, 1989.     

Development of a finite element model of metal powder compaction process at elevated temperature

This paper presents the finite element modelling of metal powder compaction process at elevated temperature. In the modelling, the behaviour of powder is assumed to be rate independent thermo-elastoplastic material where the material constitutive laws are derived based on a continuum mechanics approach. The deformation process of metal powder has been described by a large displacement based finite element formulation. The Elliptical Cap yield model has been used to represent the deformation behaviour of the powder mass during the compaction process. This yield model was tested and found to be appropriate to represent the compaction process. The staggered-incremental-iterative solution strategy has been established to solve the non-linearity in the systems of equations. Some numerical simulation results were validated through experimentation, where a good agreement was found between the numerical simulation results and the experimental data.     

Using number fields to compute logarithms in finite fields

We describe an adaptation of the number field sieve to the problem of computing logarithms in a finite field. We conjecture that the running time of the algorithm, when restricted to finite fields of an arbitrary but fixed degree, is where is the cardinality of the field, and the is for . The number field sieve factoring algorithm is conjectured to factor a number the size of in the same amount of time.

     

β-Expansions in algebraic function fields over finite fields

The present paper deals with an algebraic function field analogue of β-expansions of real numbers. It completely characterizes the sets with eventually periodic and finite expansions. These characterizations are unknown in the real case.