1997
DOI: 10.1016/s0378-4371(97)00312-9
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Groundstate threshold in triangular anisotropic +/−J Ising models

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Cited by 8 publications
(4 citation statements)
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“…Further, note that p c and ν found here agree well with the values p c = 0.1583 (6) and ν = 1.47(9) that characterize the negativeweight percolation of loops on 2d lattice graphs with a honeycomb geometry and fully periodic boundary conditions [13]. Finally, the location of the critical point obtained here via FSS analysis is close to the theoretical prediction p c,tr = 0.15, that was obtained for systems with fully periodic boundary conditions using the adjoined problem approach [24,16].…”
Section: Discussionsupporting
confidence: 89%
See 1 more Smart Citation
“…Further, note that p c and ν found here agree well with the values p c = 0.1583 (6) and ν = 1.47(9) that characterize the negativeweight percolation of loops on 2d lattice graphs with a honeycomb geometry and fully periodic boundary conditions [13]. Finally, the location of the critical point obtained here via FSS analysis is close to the theoretical prediction p c,tr = 0.15, that was obtained for systems with fully periodic boundary conditions using the adjoined problem approach [24,16].…”
Section: Discussionsupporting
confidence: 89%
“…In this regard, we obtain a highly precise estimate of the critical point for the triangular lattice geometry and we verify the critical exponents obtained earlier for the RBIM on the planar square lattice [14,15]. Finally, we contrast our nu- merical results with previous simulations and presumably exact results [16].…”
Section: Introductionsupporting
confidence: 85%
“…If one is interested in obtaining the partition sum, without obtaining spin configurations, one can also treat systems with full periodic boundary conditions in polynomial time, by using transfer-matrix approaches 24,25,26,27 , but the running time is again strongly increasing, limiting the investigations to small systems. The most recent studies are based on matching algorithms 29,30,31,32,33,34,35,36,37 , while other exact approaches can be found in Refs. 38,39,40 .…”
Section: Algorithmmentioning
confidence: 99%
“…Our threedimensional model thus has a droplet like behavior at finite length scales, but its energy landscape at large length scales is as predicted by mean field.The model -We consider a system arising in combinatorial optimization: the minimum matching problem (MMP) [7]. This choice is motivated by the following properties: (i) the problem of finding ground states of two-dimensional spin glasses can be mapped to a MMP [8] (see [9] for recent developments); (ii) we are able to compute quickly and exactly the ground state and the excited states of the MMP for any realization of the disorder; (iii) a droplet picture can be constructed quite naturally; (iv) the replica approach has been used to solve a mean field approximation of the model [10].Consider N points (N even) and the set of "distances" between them. These distances define the instance, that 1…”
mentioning
confidence: 99%