Recurrent random walks and the absence of continuous symmetry breaking on graphs

1994 ◽  
Vol 75 (1-2) ◽  
pp. 153-165 ◽  
Author(s):  
Franz Merkl ◽  
Herbert Wagner
Keyword(s):  
Symmetry Breaking ◽  
Random Walks ◽  
Continuous Symmetry

Phase Transitions and Continuous Symmetry Breaking

1976 ◽  
Vol 36 (14) ◽  
pp. 804-806 ◽  
Author(s):  
J. Fröhlich ◽  
B. Simon ◽  
T. Spencer
Keyword(s):  
Phase Transitions ◽  
Symmetry Breaking ◽  
Continuous Symmetry

scholarly journals 300 nm bandwidth adiabatic SOI polarization splitter-rotators exploiting continuous symmetry breaking

2015 ◽  
Vol 23 (15) ◽  
pp. 19261 ◽  
Author(s):  
Luciano Socci ◽  
Vito Sorianello ◽  
Marco Romagnoli
Keyword(s):  
Symmetry Breaking ◽  
Polarization Splitter ◽  
Continuous Symmetry

scholarly journals Average properties of combinatorial problems and thermodynamics of spin models on graphs

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Alessandro Vezzani ◽  
Davide Cassi ◽  
Raffaella Burioni
Keyword(s):  
Random Walks ◽  
Spontaneous Magnetization ◽  
Discrete Symmetry ◽  
Combinatorial Problems ◽  
Infinite Graphs ◽  
Continuous Symmetry ◽  
Spin Models ◽  
Graph Topology ◽  
International Audience ◽  
Classical Spin Models

International audience The study of thermodynamic properties of classical spin models on infinite graphs naturally leads to consider the new combinatorial problems of random-walks and percolation on the average. Indeed, spinmodels with O(n) continuous symmetry present spontaneous magnetization only on transient on the average graphs, while models with discrete symmetry (Ising and Potts) are spontaneously magnetized on graphs exhibiting percolation on the average. In this paper we define the combinatorial problems on the average, showing that they give rise to classifications of graph topology which are different from the ones obtained in usual (local) random-walks and percolation. Furthermore, we illustrate the theorem proving the correspondence between Potts model and average percolation.

Effect of symmetry breaking on two-dimensional random walks

1995 ◽  
Vol 52 (4) ◽  
pp. 4516-4519 ◽  
Author(s):  
P. Alpatov ◽  
L. E. Reichl
Keyword(s):  
Symmetry Breaking ◽  
Random Walks ◽  
Two Dimensional
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