scholarly journals POSSIBLY EXACT SOLUTION FOR THE MULTICRITICAL POINT OF FINITE-DIMENSIONAL SPIN GLASSES

2006 ◽  
Author(s):  
HIDETOSHI NISHIMORI ◽  
KOUJIN TAKEDA ◽  
TOMOHIRO SASAMOTO
Keyword(s):  
Exact Solution ◽  
Spin Glasses ◽  
Multicritical Point ◽  
Finite Dimensional

scholarly journals POSSIBLY EXACT SOLUTION FOR THE MULTICRITICAL POINT OF FINITE-DIMENSIONAL SPIN GLASSES

2006 ◽  
Vol 20 (19) ◽  
pp. 2805-2813
Author(s):  
HIDETOSHI NISHIMORI ◽  
KOUJIN TAKEDA ◽  
TOMOHIRO SASAMOTO
Keyword(s):  
Phase Diagram ◽  
Exact Solution ◽  
Spin Glasses ◽  
Lattice Gauge Theory ◽  
Square Lattice ◽  
Temperature Transition ◽  
Multicritical Point ◽  
Random Lattice ◽  
Finite Dimensional ◽  
Lattice Gauge

After briefly describing the present status of the spin glass theory, we present a conjecture on the exact location of the multicritical point in the phase diagram of finite-dimensional spin glasses. The theory enables us to understand in a unified way many numerical results for two-, three- and four-dimensional models including the ±J Ising model, random Potts model, random lattice gauge theory, and random Zq model. It is also suggested from the same theoretical framework that models with symmetric distribution of randomness in exchange interaction have no finite-temperature transition on the square lattice.

scholarly journals Exact location of the multicritical point for finite-dimensional spin glasses: a conjecture

2005 ◽  
Vol 38 (17) ◽  
pp. 3751-3774 ◽  
Author(s):  
Koujin Takeda ◽  
Tomohiro Sasamoto ◽  
Hidetoshi Nishimori
Keyword(s):  
Spin Glasses ◽  
Multicritical Point ◽  
Exact Location ◽  
Finite Dimensional

scholarly journals Multicritical point of spin glasses

2010 ◽  
Vol 389 (15) ◽  
pp. 2907-2910 ◽  
Author(s):  
Hidetoshi Nishimori ◽  
Masayuki Ohzeki
Keyword(s):  
Spin Glasses ◽  
Multicritical Point

scholarly journals On targeting an integral funnel of control system at a target set in the phase space

2020 ◽  
Vol 56 ◽  
pp. 79-101
Author(s):  
V.N. Ushakov ◽  
A.V. Ushakov
Keyword(s):  
Exact Solution ◽  
Control System ◽  
Phase Space ◽  
Euclidean Space ◽  
Time Moment ◽  
Dimensional Euclidean Space ◽  
Time Interval ◽  
Finite Dimensional ◽  
Approximate Construction ◽  
Target Set

A control system in finite-dimensional Euclidean space is considered. On a given time interval, we investigate the problem of constructing an integral funnel for which a section corresponding to the last time moment of interval is equal to a target set in a phase space. Since the exact solution of such a funnel is possible only in rare cases, the question of the approximate construction of an integral funnel is being studied.

scholarly journals Duality in Finite-Dimensional Spin Glasses

2006 ◽  
Vol 126 (4-5) ◽  
pp. 977-986 ◽  
Author(s):  
Hidetoshi Nishimori
Keyword(s):  
Spin Glasses ◽  
Finite Dimensional

ON EXACT SOLUTION OF OPTIMIZATION TASK GENERATED BY THE LAPLACE EQUATION

2018 ◽  
pp. 466-472
Author(s):  
Asaad Naser Mzedawee
Keyword(s):  
Exact Solution ◽  
Laplace Equation ◽  
Existence And Uniqueness ◽  
Parameter Family ◽  
Two Dimensional ◽  
Special Sequence ◽  
Optimization Task ◽  
Finite Dimensional ◽  
Residual Functional

A one-parameter family of finite-dimensional spaces consisting of special two-dimensional splines of Lagrangian type is defined (the parameter N is related to the dimension of the space). The Laplace equation generates in each such space the problem of minimizing the residual functional. The existence and uniqueness of optimal splines are proved. For their coefficients and residuals, exact formulas are obtained. It is shown that with increasing N; the minimum of the residual functional is O(N^(-5) ); and the special sequence consisting of optimal splines is fundamental.

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