On analyticity with respect to the replica number in random energy models: I. An exact expression for the moment of the partition function

We derive an exact expression for the partition function of two spin-1/2 Tomonaga–Luttinger chains, and obtain the renormalization group equation for the normal state. Anderson's confinement is then discussed. We find that spin–charge separation is irrelevant to the confinement.

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Liouville Field Theory and Log-Correlated Random Energy Models

Physical Review Letters ◽

10.1103/physrevlett.118.090601 ◽

2017 ◽

Vol 118 (9) ◽

Cited By ~ 5

Author(s):

Xiangyu Cao ◽

Alberto Rosso ◽

Raoul Santachiara ◽

Pierre Le Doussal

Keyword(s):

Field Theory ◽

Random Energy ◽

Energy Models ◽

Liouville Field Theory

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Derrida's Generalized Random Energy models 2: models with continuous hierarchies

Annales de l Institut Henri Poincaré Probabilités et Statistiques ◽

10.1016/j.anihpb.2003.09.003 ◽

2004 ◽

Vol 40 (4) ◽

pp. 481-495 ◽

Cited By ~ 26

Author(s):

A BOVIER

Keyword(s):

Random Energy ◽

Energy Models

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The algorithmic hardness threshold for continuous random energy models

Mathematical Statistics and Learning ◽

10.4171/msl/12 ◽

2020 ◽

Vol 2 (1) ◽

pp. 77-101

Author(s):

Louigi Addario-Berry ◽

Pascal Maillard

Keyword(s):

Random Energy ◽

Energy Models

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The diamagnetism of quasi-bound conduction electrons

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100028383 ◽

1953 ◽

Vol 49 (2) ◽

pp. 292-298 ◽

Cited By ~ 46

Author(s):

A. H. Wilson

Keyword(s):

Magnetic Field ◽

Partition Function ◽

Power Series ◽

Density Matrix ◽

Complete Solution ◽

Exact Expression ◽

Free Electrons ◽

Conduction Electrons ◽

Image Position ◽

Bound Electrons

The diamagnetism of the conduction electrons gives rise to some of the most difficult problems in the theory of metals, the complete solution of which has not yet been found. Formally, the problem is equivalent to determining the density matrixand the exact expression for ψ(r′, r, γ) for perfectly free electrons in a constant magnetic field H has recently been found by Sondheimer and Wilson(2). The extension of the theory to deal with quasi-bound electrons for all values of H seems to be out of the question, but an approximate partition function was given by Peierls (1), excluding terms of higher order than H2. In The theory of metals ((3), referred to as T.M.) I gave a more powerful and simpler method of dealing with the problem, based upon the properties of ψ(r′, r, γ), but since the solution was obtained as a power series in μ0Hγ, where it could at best determine only the normal diamagnetism.

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