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 Updates on the QCD phase diagram from lattice

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Sayantan Sharma
Keyword(s):  
Phase Diagram ◽  
Lattice Gauge Theory ◽  
Topological Properties ◽  
Chiral Phase ◽  
Qcd Phase Diagram ◽  
Qcd Vacuum ◽  
Lattice Gauge ◽  
Massless Quark ◽  
Quark Flavors

AbstractDifferent aspects of the phase diagram of strongly interacting matter described by quantum chromodynamics (QCD), which have emerged from the recent studies using lattice gauge theory techniques, are discussed. A special emphasis is given on understanding the role of the anomalous axial U(1) symmetry in determining the order of the finite temperature chiral phase transition in QCD with two massless quark flavors and tracing its origin to the topological properties of the QCD vacuum.

scholarly journals EXACT SOLUTION OF INDUCED LATTICE GAUGE THEORY AT LARGE-N

1993 ◽  
Vol 08 (04) ◽  
pp. 359-371 ◽  
Author(s):  
A.A. MIGDAL
Keyword(s):  
Exact Solution ◽  
Gauge Theory ◽  
Scalar Field ◽  
Lattice Gauge Theory ◽  
Arbitrary Dimension ◽  
Adjoint Representation ◽  
Lattice Gauge ◽  
Large N ◽  
Proposed Model ◽  
The Continuum

We find the exact solution of a recently proposed model of the lattice gauge theory induced by heavy scalar field in adjoint representation at N=∞ for arbitrary dimension D. The nonlinear integral equation for the gauge invariant density of eigenvalues of the vacuum average of the scalar field is derived. In the continuum limit, the density grows as ɸα where [Formula: see text] arccos [Formula: see text].

scholarly journals PHASE DIAGRAM OF A LOOP ON THE SQUARE LATTICE

1999 ◽  
Vol 10 (01) ◽  
pp. 301-308 ◽  
Author(s):  
WENAN GUO ◽  
HENK W. J. BLÖTE ◽  
BERNARD NIENHUIS
Keyword(s):  
Phase Diagram ◽  
Transfer Matrix ◽  
Critical Line ◽  
Finite Size ◽  
Square Lattice ◽  
Size Analysis ◽  
Loop Model ◽  
Multicritical Point ◽  
Variable Parameters ◽  
Special Case

The phase diagram of the O (n) model, in particular the special case n=0, is studied by means of transfer-matrix calculations on the loop representation of the O (n) model. The model is defined on the square lattice; the loops are allowed to collide at the lattice vertices, but not to intersect. The loop model contains three variable parameters that determine the loop density or temperature, the energy of a bend in a loop, and the interaction energy of colliding loop segments. A finite-size analysis of the transfer-matrix results yields the phase diagram in a special plane of the parameter space. These results confirm the existence of a multicritical point and an Ising-like critical line in the low-temperature O (n) phase.

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
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