Mixing in time and space for lattice spin systems: A combinatorial view

2004 ◽  
Vol 24 (4) ◽  
pp. 461-479 ◽  
Author(s):  
Martin Dyer ◽  
Alistair Sinclair ◽  
Eric Vigoda ◽  
Dror Weitz
Keyword(s):  
Spin Systems ◽  
Time And Space ◽  
Lattice Spin ◽  
Lattice Spin Systems

scholarly journals Approximate Tensorization of the Relative Entropy for Noncommuting Conditional Expectations

2021 ◽  
Author(s):  
Ivan Bardet ◽  
Ángela Capel ◽  
Cambyse Rouzé
Keyword(s):  
Relative Entropy ◽  
Von Neumann Algebras ◽  
Logarithmic Sobolev Inequality ◽  
Spin Systems ◽  
Von Neumann ◽  
Strong Subadditivity ◽  
Finite Dimensional ◽  
Lattice Spin ◽  
Lattice Spin Systems ◽  
Conditional Expectations

AbstractIn this paper, we derive a new generalisation of the strong subadditivity of the entropy to the setting of general conditional expectations onto arbitrary finite-dimensional von Neumann algebras. This generalisation, referred to as approximate tensorization of the relative entropy, consists in a lower bound for the sum of relative entropies between a given density and its respective projections onto two intersecting von Neumann algebras in terms of the relative entropy between the same density and its projection onto an algebra in the intersection, up to multiplicative and additive constants. In particular, our inequality reduces to the so-called quasi-factorization of the entropy for commuting algebras, which is a key step in modern proofs of the logarithmic Sobolev inequality for classical lattice spin systems. We also provide estimates on the constants in terms of conditions of clustering of correlations in the setting of quantum lattice spin systems. Along the way, we show the equivalence between conditional expectations arising from Petz recovery maps and those of general Davies semigroups.

scholarly journals Geometric criterion for solvability of lattice spin systems

2020 ◽  
Vol 102 (24) ◽  
Author(s):  
Masahiro Ogura ◽  
Yukihisa Imamura ◽  
Naruhiko Kameyama ◽  
Kazuhiko Minami ◽  
Masatoshi Sato
Keyword(s):  
Spin Systems ◽  
Geometric Criterion ◽  
Lattice Spin ◽  
Lattice Spin Systems

scholarly journals Nonconventional averages along arithmetic progressions and lattice spin systems

2012 ◽  
Vol 23 (3) ◽  
pp. 589-602 ◽  
Author(s):  
Gioia Carinci ◽  
Jean-René Chazottes ◽  
Cristian Giardinà ◽  
Frank Redig
Keyword(s):  
Spin Systems ◽  
Arithmetic Progressions ◽  
Lattice Spin ◽  
Lattice Spin Systems ◽  
Nonconventional Averages

Link formulation of lattice spin systems

1984 ◽  
Vol 30 (8) ◽  
pp. 1775-1781 ◽  
Author(s):  
Ghassan G. Batrouni ◽  
M. B. Halpern
Keyword(s):  
Spin Systems ◽  
Lattice Spin ◽  
Lattice Spin Systems
Sign in / Sign up

Export Citation Format

Share Document