scholarly journals Directed Polymers and Interfaces in Disordered Media

Polymers ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 1066
Author(s):  
Róbinson J. Acosta Diaz ◽  
Christian D. Rodríguez-Camargo ◽  
Nami F. Svaiter
Keyword(s):  
Field Theory ◽  
Free Energy ◽  
Partition Function ◽  
Saddle Point ◽  
Finite Temperature ◽  
Series Representation ◽  
Replica Method ◽  
Quenched Disorder ◽  
Directed Polymers ◽  
Disordered Media

We consider field theory formulation for directed polymers and interfaces in the presence of quenched disorder. We write a series representation for the averaged free energy, where all the integer moments of the partition function of the model contribute. The structure of field space is analysed for polymers and interfaces at finite temperature using the saddle-point equations derived from each integer moments of the partition function. For the case of an interface we obtain the wandering exponent ξ = ( 4 − d ) / 2 , also obtained by the conventional replica method for the replica symmetric scenario.

REGULARIZATION OF GENERAL MULTIDIMENSIONAL EPSTEIN ZETA-FUNCTIONS

1989 ◽  
Vol 01 (01) ◽  
pp. 113-128 ◽  
Author(s):  
E. ELIZALDE ◽  
A. ROMEO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Partition Function ◽  
Zeta Function ◽  
Finite Temperature ◽  
Casimir Effect ◽  
Zeta Functions ◽  
Quantum Field ◽  
Type Formula

We study expressions for the regularization of general multidimensional Epstein zeta-functions of the type [Formula: see text] After reviewing some classical results in the light of the extended proof of zeta-function regularization recently obtained by the authors, approximate but very quickly convergent expressions for these functions are derived. This type of analysis has many interesting applications, e.g. in any quantum field theory defined in a partially compactified Euclidean spacetime or at finite temperature. As an example, we obtain the partition function for the Casimir effect at finite temperature.

scholarly journals Effective electromagnetic lagrangian at finite temperature and density in the electroweak model

Open Physics ◽  
2011 ◽  
Vol 9 (4) ◽  
Author(s):  
Andrea Erdas
Keyword(s):  
Magnetic Field ◽  
Free Energy ◽  
Partition Function ◽  
Field Strength ◽  
Constant Magnetic Field ◽  
Finite Temperature ◽  
Weak Coupling ◽  
Weak Coupling Limit ◽  
Effective Coupling ◽  
Electroweak Model

AbstractUsing the exact propagators in a constant magnetic field, the effective electromagnetic lagrangian at finite temperature and density is calculated to all orders in the field strength B within the framework of the complete electroweak model, in the weak coupling limit. The partition function and free energy are obtained explicitly and the finite temperature effective coupling is derived in closed form. Some implications of this result, potentially interesting to astrophysics and cosmology, are discussed.

scholarly journals The distributional zeta-function in disordered field theory

2016 ◽  
Vol 31 (25) ◽  
pp. 1650144 ◽  
Author(s):  
B. F. Svaiter ◽  
N. F. Svaiter
Keyword(s):  
Field Theory ◽  
Free Energy ◽  
Partition Function ◽  
Zeta Function ◽  
Complex Function ◽  
Function Technique ◽  
Dimensional Euclidean Space ◽  
Basic Tool ◽  
Disordered System ◽  
Text Model

In this paper, we present a new mathematical rigorous technique for computing the average free energy of a disordered system with quenched randomness, using the replicas. The basic tool of this technique is a distributional zeta-function, a complex function whose derivative at the origin yields the average free energy of the system as the sum of two contributions: the first one is a series in which all the integer moments of the partition function of the model contribute; the second one, which cannot be written as a series of the integer moments, can be made as small as desired. This result supports the use of integer moments of the partition function, computed via replicas, for expressing the average free energy of the system. One advantage of the proposed formalism is that it does not require the understanding of the properties of the permutation group when the number of replicas goes to zero. Moreover, the symmetry is broken using the saddle-point equations of the model. As an application for the distributional zeta-function technique, we obtain the average free energy of the disordered [Formula: see text] model defined in a [Formula: see text]-dimensional Euclidean space.

scholarly journals A FINITE TEMPERATURE PERIODIC STRUCTURE IN (SUPER)STRING THEORY

1993 ◽  
Vol 08 (12) ◽  
pp. 1131-1138 ◽  
Author(s):  
A. A. BYTSENKO ◽  
E. ELIZALDE ◽  
S. D. ODINTSOV ◽  
S. ZERBINI
Keyword(s):  
Free Energy ◽  
String Theory ◽  
Analytic Continuation ◽  
Explicit Form ◽  
Periodic Structure ◽  
Finite Temperature ◽  
Laurent Series ◽  
Series Representation ◽  
Additional Result

Using a Laurent series representation for the (super)string one-loop free energy, an explicit form for the analytic continuation of the Laurent series beyond the critical (Hagedorn) temperature is obtained. As an additional result, a periodic structure in (super)string thermodynamics is found. A brief physical discussion about the origin and meaning of such a structure is carried out.

scholarly journals From Brownian Motion Formalism to Fluctuation-Induced Force in a General Fluctuating Medium

2018 ◽  
Vol 17 (03) ◽  
pp. 1850020
Author(s):  
Fardin Kheirandish
Keyword(s):  
Free Energy ◽  
Brownian Motion ◽  
Partition Function ◽  
General Expression ◽  
Finite Temperature ◽  
Microscopic Approach ◽  
Quantum Brownian Motion ◽  
Anisotropic Matter

Starting from a microscopic approach and using the formalism of quantum Brownian motion, partition function of a system composed of two separated pieces of anisotropic matter and a fluctuating medium in finite temperature is obtained rigorously. A general expression for fluctuation-induced free energy between the separated anisotropic pieces of matter is obtained and it is shown that in the framework of induced-force, the free energy of mean-force and effective free energy are equivalent.

PERTURBATIVE RESULTS OF COLLECTIVE STRING FIELD THEORY

1991 ◽  
Vol 06 (35) ◽  
pp. 3199-3212 ◽  
Author(s):  
KRESIMIR DEMETERFI ◽  
ANTAL JEVICKI ◽  
JOĀO P. RODRIGUES
Keyword(s):  
Field Theory ◽  
Free Energy ◽  
Scattering Amplitudes ◽  
Ground State Energy ◽  
String Field Theory ◽  
Ground State ◽  
Finite Temperature ◽  
State Energy ◽  
Tree Level ◽  
Self Energy

We present a summary of perturbative results obtained in the framework of collective string field theory. We discuss computations of tree-level scattering amplitudes, loop corrections to tachyon self-energy, ground state energy and finite temperature free energy. A comparison with results obtained in different approaches is given. We also discuss the physical implications of our results.

A canonical ensemble derivation of the McMillan-Mayer solution theory

1983 ◽  
Vol 48 (10) ◽  
pp. 2888-2892 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Energy Function ◽  
Special Function ◽  
Helmholtz Free Energy ◽  
Canonical Ensemble ◽  
Free Energy Function ◽  
Solution Theory ◽  
Pure Solvent ◽  
The Common

A special free energy function is defined for a solution in the osmotic equilibrium with pure solvent. The partition function of the solution is derived at the McMillan-Mayer level and it is related to this special function in the same manner as the common partition function of the system to its Helmholtz free energy.

scholarly journals Boundary conditions in topological AdS4/CFT3

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Pietro Benetti Genolini ◽  
Matan Grinberg ◽  
Paul Richmond
Keyword(s):  
Field Theory ◽  
Free Energy ◽  
Boundary Conditions ◽  
Smooth Solution ◽  
Three Dimensional ◽  
Field Theories ◽  
Legendre Transformation ◽  
Generating Functional ◽  
Holographic Duals

Abstract We revisit the construction in four-dimensional gauged Spin(4) supergravity of the holographic duals to topologically twisted three-dimensional $$ \mathcal{N} $$ N = 4 field theories. Our focus in this paper is to highlight some subtleties related to preserving supersymmetry in AdS/CFT, namely the inclusion of finite counterterms and the necessity of a Legendre transformation to find the dual to the field theory generating functional. Studying the geometry of these supergravity solutions, we conclude that the gravitational free energy is indeed independent from the metric of the boundary, and it vanishes for any smooth solution.

scholarly journals The bulk, surface and corner free energies of the anisotropic triangular Ising model

2020 ◽  
Vol 476 (2234) ◽  
pp. 20190713
Author(s):  
Rodney J. Baxter
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Partition Function ◽  
Temperature Series ◽  
Isotropic Case ◽  
Series Expansions ◽  
Exact Results ◽  
Free Energies ◽  
Bulk Surface ◽  
Bulk Free Energy

We consider the anisotropic Ising model on the triangular lattice with finite boundaries, and use Kaufman’s spinor method to calculate low-temperature series expansions for the partition function to high order. From these, we can obtain 108-term series expansions for the bulk, surface and corner free energies. We extrapolate these to all terms and thereby conjecture the exact results for each. Our results agree with the exactly known bulk-free energy and with Cardy and Peschel’s conformal invariance predictions for the dominant behaviour at criticality. For the isotropic case, they also agree with Vernier and Jacobsen’s conjecture for the 60 ° corners.

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