Spin models for link invariants

1995 ◽  
pp. 71-102 ◽  
Author(s):  
François Jaeger
Keyword(s):  
Spin Models ◽  
Link Invariants

scholarly journals Evidence of exactness of the mean-field theory in the nonextensive regime of long-range classical spin models

2000 ◽  
Vol 61 (17) ◽  
pp. 11521-11528 ◽  
Author(s):  
Sergio A. Cannas ◽  
A. C. N. de Magalhães ◽  
Francisco A. Tamarit
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spin Models ◽  
Classical Spin ◽  
The Mean ◽  
Classical Spin Models

scholarly journals Nanolaser-based emulators of spin Hamiltonians

Nanophotonics ◽  
2020 ◽  
Vol 9 (13) ◽  
pp. 4193-4198 ◽  
Author(s):  
Midya Parto ◽  
William E. Hayenga ◽  
Alireza Marandi ◽  
Demetrios N. Christodoulides ◽  
Mercedeh Khajavikhan
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Exchange Interactions ◽  
Np Hard ◽  
Spin Models ◽  
Geometric Frustration ◽  
Spin Hamiltonians ◽  
Hard Problems ◽  
On Chip ◽  
Classical Spin Models

AbstractFinding the solution to a large category of optimization problems, known as the NP-hard class, requires an exponentially increasing solution time using conventional computers. Lately, there has been intense efforts to develop alternative computational methods capable of addressing such tasks. In this regard, spin Hamiltonians, which originally arose in describing exchange interactions in magnetic materials, have recently been pursued as a powerful computational tool. Along these lines, it has been shown that solving NP-hard problems can be effectively mapped into finding the ground state of certain types of classical spin models. Here, we show that arrays of metallic nanolasers provide an ultra-compact, on-chip platform capable of implementing spin models, including the classical Ising and XY Hamiltonians. Various regimes of behavior including ferromagnetic, antiferromagnetic, as well as geometric frustration are observed in these structures. Our work paves the way towards nanoscale spin-emulators that enable efficient modeling of large-scale complex networks.

scholarly journals FROM RIBBON CATEGORIES TO GENERALIZED YANG–BAXTER OPERATORS AND LINK INVARIANTS (AFTER KITAEV AND WANG)

2013 ◽  
Vol 24 (01) ◽  
pp. 1250126 ◽  
Author(s):  
SEUNG-MOON HONG
Keyword(s):  
The Other ◽  
Polynomial Invariant ◽  
Link Invariants ◽  
Fusion Categories ◽  
New Family ◽  
Kauffman Polynomial ◽  
Twist Structure

We consider two approaches to isotopy invariants of oriented links: one from ribbon categories and the other from generalized Yang–Baxter (gYB) operators with appropriate enhancements. The gYB-operators we consider are obtained from so-called gYBE objects following a procedure of Kitaev and Wang. We show that the enhancement of these gYB-operators is canonically related to the twist structure in ribbon categories from which the operators are produced. If a gYB-operator is obtained from a ribbon category, it is reasonable to expect that two approaches would result in the same invariant. We prove that indeed the two link invariants are the same after normalizations. As examples, we study a new family of gYB-operators which is obtained from the ribbon fusion categories SO (N)2, where N is an odd integer. These operators are given by 8 × 8 matrices with the parameter N and the link invariants are specializations of the two-variable Kauffman polynomial invariant F.

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