We investigate thermodynamical properties of quantum electrodynamics in 1 + 1 dimensions (QED1+1). Discrete light cone quantization is used to compute the partition function of the canonical ensemble and the thermodynamical potential. The potential is evaluated for different system sizes and coupling strengths. We perform the continuum limit and the thermodynamical limit and present basic therm...

We investigate the back-reaction effect of the quantum field on the topological degrees of freedom in (2+1)-dimensional toroidal universe, M ≃ T 2 × R. Constructing a homogeneous model of the toroidal universe, we examine explicitly the back-reaction effect of the Casimir energy of a massless, conformally coupled scalar field, with a conformal vacuum. The back-reaction causes an instability of ...

We investigate the back-reaction e ect of the quantum eld on the topological degrees of freedom in (2+1)-dimensional toroidal universe, M ' T 2 R. Constructing a homogeneous model of the toroidal universe, we examine explicitly the back-reaction e ect of the Casimir energy of a massless, conformally coupled scalar eld, with a conformal vacuum. The back-reaction causes an instability of the univ...

The grand canonical partition functions for primitive droplet nucleation models with an excess energy ǫ n = −ˆµ n + σ n 1−η , η = 1/d, for droplets of n constituents in d dimensions are calculated exactly in closed form in the cases d = 2 and 3 for all (complex) ˆ µ by exploiting the fact that the partition functions obey simple linear PDE.

The canonical coding partition of a set of words is the finest partition such that the words contained in at least two factorizations of a same sequence belong to a same class. In the case the set is not uniquely decipherable, it partitions the set into one unambiguous class and other parts that localize the ambiguities in the factorizations of finite

The application of a Monte Carlo approach for computing the configurational free energy of chains is described. Whereas the effectiveness of the previous Monte Carlo methods is limited to the systems in which the energies of the stares (configurations) are not far from zero, the present approach can yield accurate estimates of the free energy of the systems with large configurational energy. Th...

We apply the Ginzburg criterion to the dimer problem and we solve the apparent contradiction of a system with mean field α = 12 , the typical value of tricritical systems, and upper critical dimension Dcr = 6. We find that the system has upper critical dimensionDcr = 6 , while for D ≤ 4 it should undergo a first order phase transition. We comment on the latter wrong result examining the approxi...

In 1918, Hardy and Ramanujan wrote their landmark paper deriving the asymptotic formula for the partition function. The paper however was fundamental for another reason, namely for introducing the circle method in questions of additive number theory. Though this method is powerful, it is often difficult and technically complicated to employ. In 2011, Bruinier and Ono discovered a new algebraic ...

Stanley defined a partition function t(n) as the number of partitions λ of n such that the number of odd parts of λ is congruent to the number of odd parts of the conjugate partition λ modulo 4. We show that t(n) equals the number of partitions of n with an even number of hooks of even length. We derive a closed-form formula for the generating function for the numbers p(n)− t(n). As a consequen...

Binary mixtures of surfactants build a binary mixed micelle in which the ratio usually differs from initial their mixture. The thermodynamic stabilization micellar pseudophase about hypothetical ideal state (intermolecular interactions between different particles and conformational states are identical to those monocomponent states) is described by molar excess Gibbs free energy (gE). dependenc...