Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1110.6034

A combinatorial proof of tree decay of semi-invariants

L. Bertini·Emilio N. M. Cirillo·E. Olivieri
View original source ↗Read source document ↗Export metadata ↓

Abstract

We consider finite range Gibbs fields and provide a purely combinatorial proof of the exponential tree decay of semi--invariants, supposing that the logarithm of the partition function can be expressed as a sum of suitable local functions of the boundary conditions. This hypothesis holds for completely analytical Gibbs fields; in this context the tree decay of semi--invariants has been proven via analyticity arguments. However the combinatorial proof given here can be applied also to the more complicated case of disordered systems in the so called Griffiths' phase when analyticity arguments fail.

Explore related subjects

cond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

L. Bertini, Emilio N. M. Cirillo, E. Olivieri. 2011-10-27. A combinatorial proof of tree decay of semi-invariants. https://doi.org/10.1023/b%3Ajoss.0000019813.58778.bf

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The free energy of the square lattice Ising model with interactions alternating in horizontal and vertical directions

The free energy of the Ising model on the square lattice with alternating interactions in both horizontal and vertical directions is exactly derived. This model is distinct from the checkerboard Ising model. The result includes Onsager's free energy as a special case, and also includes Lee-Yang's free energy with an imaginary field, and relates these two solutions via continuous parameters. The result includes a generalization of Lee-Yang's result to cases with four different couplings. It is also derived that each imaginary magnetic field $iπ/2$ applied to a lattice site corresponds to a single frustrated square in its dual lattice.

cond-mat.stat-mech↗
arXiv2026

Ideal heat engine cycles at maximal efficiency -- the ideal gas and beyond

Given a particular heat engine cycle, what is the optimal working medium that results in the highest efficiency? While one might jump to the conclusion that it must surely be the ideal gas, the situation is actually more intricate. Starting with a general Helmholtz potential that depends polynomially on molar volume and temperature we derive exact expressions for the ideal Stirling, Otto, and Brayton cycles. We find that for the thermodynamic systems described by our ansatz for the Helmholtz potential the maximal efficiency is achieved, if the working medium is described by a fundamental relation linear in temperature. This includes the ideal gas, but also classical harmonic oscillators and phenomenological models of the rubber band.

cond-mat.stat-mech↗
arXiv2026

Local Detailed Balance in the Lorenz Model: Replaces the Butterfly with Frenetic Bursting

The Lorenz system is the canonical low-order model of convective instability, yet its dissipative and driving terms have never been checked against, nor constructed from, an explicit thermodynamic bookkeeping. We derive a modification that satisfies the local-detailed-balance condition for macroscopic relaxation toward nonequilibrium steady states, thereby identifying the thermodynamic force, entropy-production rate and frenesy of the resulting flow. The resulting model produces a transition from a quiescent fixed point to a robust, large-amplitude relaxation oscillation, closely analogous to recharge-discharge oscillator paradigms used for the El Nino-Southern Oscillation. The system alternates between a long, nearly reversible recharge phase and a brief, violently frenetic discharge burst, during which essentially all of the cycle's activity and entropy production is concentrated.

cond-mat.stat-mech↗