Latest Research Papers In Condensed Matter Physics | (Cond-Mat.Stat-Mech) 2019-02-22
Statistical Mechanics
The random field XY model on sparse random graphs shows replica symmetry breaking and marginally stable ferromagnetism (1902.07132v2)
Cosimo Lupo, Giorgio Parisi, Federico Ricci-Tersenghi
2019-02-19
The ferromagnetic XY model on sparse random graphs in a randomly oriented field is analyzed via the belief propagation algorithm. At variance with the fully connected case and with the random field Ising model on the same topology, we find strong evidences of a tiny region with Replica Symmetry Breaking (RSB) in the limit of very low temperatures. This RSB phase is robust against different choices of the external field direction, while it rapidly vanishes when increasing the graph mean degree, the temperature or the directional bias in the external field. The crucial ingredients to have such a RSB phase seem to be the continuous nature of vector spins, mostly preserved by the O(2)-invariant random field, and the strong spatial heterogeneity, due to graph sparsity. We also uncover that the ferromagnetic phase can be marginally stable despite the presence of the random field. Finally, we study the proper correlation functions approaching the critical points to identify the ones that become more critical.
Perspective: Configurational entropy of glass-forming liquids (1902.07679v1)
Ludovic Berthier, Misaki Ozawa, Camille Scalliet
2019-02-20
The configurational entropy is one of the most important thermodynamic quantities characterizing supercooled liquids approaching the glass transition. Despite decades of experimental, theoretical, and computational investigation, a widely accepted definition of the configurational entropy is missing, its quantitative characterization remains fraud with difficulties, misconceptions and paradoxes, and its physical relevance is vividly debated. Motivated by recent computational progress, we offer a pedagogical perspective on the configurational entropy in glass-forming liquids. We first explain why the configurational entropy has become a key quantity to describe glassy materials, from early empirical observations to modern theoretical treatments. We explain why practical measurements necessarily require approximations that make its physical interpretation delicate. We then demonstrate that computer simulations have become an invaluable tool to obtain precise, non-ambiguous, and experimentally-relevant measurements of the configurational entropy. We describe a panel of available computational tools, offering for each method a critical discussion. This perspective should be useful to both experimentalists and theoreticians interested in glassy materials and complex systems.
Renormalization group analysis of the hyperbolic sine-Gordon model -- Asymptotic freedom from cosh interaction -- (1902.07642v1)
Takashi Yanagisawa
2019-02-20
We present a renormalization group analysis for the hyperbolic sine-Gordon (sinh-Gordon) model in two dimensions. We derive the renormalization group equations based on the dimensional regularization method and the Wilson method. The same equations are obtained using both these methods. We have two parameters
and
where
is related with the normalization of the action. We show that
vanishes in two dimensions.
Zero-temperature limit and Statistical Quasiparticles in Many-Body Perturbation Theory (1804.03040v2)
Corbinian Wellenhofer
2018-04-09
The order-by-order renormalization of the self-consistent mean-field potential in many-body perturbation theory for normal Fermi systems is investigated in detail. Building on previous work mainly by Balian and de Dominicis, as a key result we derive a thermodynamic perturbation series that is consistent with the adiabatic zero-temperature formalism for both isotropic and anisotropic systems and satisfies at each order and for all temperatures the thermodynamic relations associated with Fermi-liquid theory. These properties are proved to all orders.
Generalised hydrodynamics of the classical Toda system (1902.07624v1)
Benjamin Doyon
2019-02-20
We obtain the exact generalised hydrodynamics for the integrable Toda system. The Toda system can be seen in a dual way, both as a gas and as a chain. In the gas point of view, using the elastic and factorised scattering of Toda particles, we obtain the generalised free energy and exact average currents, and write down the Euler hydrodynamic equations. This is written both as a continuity equation for the density of asymptotic momenta, and in terms of normal modes. This is based on the classical thermodynamic Bethe ansatz (TBA), with a single quasiparticle type of Boltzmann statistics. By explicitly connecting chain and gas conserved densities and currents, we then derive the thermodynamics and hydrodynamics of the chain. As the gas and chain have different notions of length, they have different hydrodynamics, and in particular the velocities of normal modes differ. We also give a derivation of the classical TBA equations for the gas thermodynamics from the factorised scattering of Toda particles.
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