Thermodynamic Limit for Finite Dimensional Classical and Quantum Disordered Systems

Abstract

We provide a very simple proof for the existence of the thermodynamic limit for the quenched specific pressure for classical and quantum disordered systems on a $d$-dimensional lattice, including spin glasses. We develop a method which relies simply on Jensen's inequality and which works for any disorder distribution with the only condition (stability) that the quenched specific pressure is bounded.

14 pages. Final version, accepted for publication on Rev. Math. Phys

References in corpus (3)

• The Thermodynamic Limit in Mean Field Spin Glass Models
• Thermodynamical Limit for Correlated Gaussian Random Energy Models
• Monotonicity and Thermodynamic Limit for Short Range Disordered Models

Cited by in corpus (10)

• Thermodynamics and Universality for Mean Field Quantum Spin Glasses
• Correlation Inequalities for Quantum Spin Systems with Quenched Centered Disorder
• Universal nature of replica symmetry breaking in quantum systems with Gaussian disorder
• General properties of overlap operators in disordered quantum spin systems
• Approach to equilibrium for a class of random quantum models of infinite range
• Absence of replica symmetry breaking in the transverse and longitudinal random field Ising model
• Boundedness of Susceptibility in Spin Glass Transition of Transverse Field Mixed $p$-spin Glass Models
• No replica symmetry breaking phase in random field Ginzburg-Landau model
• Gauge theory for mixed $p$-spin glasses
• Gauge theory for quantum XYZ spin glasses