Statistical Mechanics
Optical Conductivity in an effective model for Graphene: Finite temperature corrections (1907.02017v1)
Horacio Falomir, Enrique Muñoz, Marcelo Loewe, Renato Zamora
2019-07-03
In this article, we investigate the temperature and chemical potential dependence of the optical conductivity of graphene, within a field theoretical representation in the continuum approximation, arising from an underlying tight-binding atomistic model, that includes up to next-to-nearest neighbor coupling. Our calculations allow us to obtain the dependence of the optical conductivity on frequency, temperature and finite chemical potential, generalizing our previously reported calculations at zero temperature, and reproducing the universal and experimentally verified value at zero frequency.
Quantum stochastic transport along chains (1907.01993v1)
Dekel Shapira, Doron Cohen
2019-07-03
We study the spreading along an infinite tight-binding chain, and the relaxation within a finite ring (chain with periodic boundary conditions). Specifically we address the interplay of coherent and stochastic transitions within the framework of an Ohmic master equation, which leads to a non-monotonic dependence of the current on the bias. With added disorder it becomes the quantum version of the Sinai-Derrida-Hatano-Nelson model, which features sliding and delocalization transitions. We highlight counter-intuitive enhancement of disorder due to coherent hopping.
Conformally invariant boundary conditions in the antiferromagnetic Potts model and the 
sigma model (1906.07565v2)
Niall F. Robertson, Jesper Lykke Jacobsen, Hubert Saleur
2019-06-18
We initiate a study of the boundary version of the square-lattice
-state Potts antiferromagnet, with
real, motivated by the fact that the continuum limit of the corresponding bulk model is a non-compact CFT, closely related with the
Euclidian black-hole coset model. While various types of conformal boundary conditions (discrete and continuous branes) have been formally identified for the the
algebra. The second type of CBC - which corresponds to restricting the values of the Potts spins to a subset of size
, or its complement of size
, at alternating sites along the boundary - is new, and turns out to be conformal in the antiferromagnetic case only. Using algebraic and numerical techniques, we show that the corresponding spectrum generating functions produce all the characters of discrete representations for the coset CFT. The normalizability bounds of the associated discrete states in the coset CFT are found to have a simple interpretation in terms of boundary phase transitions in the lattice model. For
, with
integer, we show also how our boundary conditions can be reformulated in terms of a RSOS height model. The spectrum generating functions are then identified with string functions of the compact
parafermion theory (with symmetry
). The new alt conditions are needed to cover all the string functions.
Resolving phase transitions with Discontinuous Galerkin methods (1903.09503v3)
Eduardo Grossi, Nicolas Wink
2019-03-22
We demonstrate the applicability and advantages of Discontinuous Galerkin (DG) schemes in the context of the Functional Renormalization Group (FRG). We investigate the
-model in the large
limit. It is shown that the flow equation for the effective potential can be cast into a conservative form. We discuss results for the Riemann problem, as well as initial conditions leading to a first and second order phase transition. In particular, we unravel the mechanism underlying first order phase transitions, based on the formation of a shock in the derivative of the effective potential.
Thermodynamics from first principles: correlations and nonextensivity (1907.01855v1)
S. N. Saadatmand, Tim Gould, E. G. Cavalcanti, J. A. Vaccaro
2019-07-03
The standard formulation of thermostatistics, featuring the Boltzmann-Gibbs-Shannon distribution and logarithmic entropy, only applies to idealized uncorrelated systems with extensive energies. In this letter, we use the fundamental principles of ergodicity, i.e. Liouville's theorem for equilibrium conditions, the self-similarity of correlations, and the existence of the thermodynamic limit to derive generalized forms of the equilibrium distribution. Significantly, our formalism provides a justification for the well-studied nonextensive thermostatistics characterized by Tsallis distribution, which it includes as a special case. We also give the complementary maximum entropy approach in which the same distributions are derived by constrained maximization of the Boltzmann-Gibbs-Shannon entropy. The consistency between the ergodic and maximum entropy approaches clarifies the use of the latter in the study of correlations and nonextensive thermodynamics.
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