scholarly journals TOWARD A PROOF OF LONG RANGE ORDER IN 4D SU(N) LATTICE GAUGE THEORY

2013 ◽  
Vol 28 (19) ◽  
pp. 1350087 ◽  
Author(s):  
MICHAEL GRADY
Keyword(s):  
Phase Transition ◽  
Gauge Theory ◽  
Long Range ◽  
Lattice Gauge Theory ◽  
Coulomb Gauge ◽  
Range Order ◽  
Spontaneous Breaking ◽  
Ferromagnetic Phase ◽  
Long Range Order ◽  
Lattice Gauge

An extended version of four-dimensional (4D) SU(2) lattice gauge theory is considered in which different inverse coupling parameters are used, [Formula: see text] for plaquettes which are purely space-like, and βV for those which involve the Euclidean time-like direction. It is shown that when βH = ∞ the partition function becomes, in the Coulomb gauge, exactly that of a set of non-interacting three-dimensional (3D) O(4) classical Heisenberg models. Long range order (LRO) at low temperatures (weak coupling) has been rigorously proven for this model. It is shown that the correlation function demonstrating spontaneous magnetization in the ferromagnetic phase is a continuous function of gH at gH = 0 and therefore, that the spontaneously broken phase enters the (βH, βV) phase plane (no step discontinuity at the edge). Once the phase transition line has entered, it can only exit at another identified edge, which requires the SU(2) gauge theory within also to have a phase transition at finite β. A phase exhibiting spontaneous breaking of the remnant symmetry left after Coulomb gauge fixing, the relevant symmetry here, is non-confining. Easy extension to the SU (N) case implies that the continuum limit of zero-temperature 4D SU (N) lattice gauge theories is not confining, in other words, gluons by themselves do not produce a confinement.

scholarly journals STRONG-COUPLING GAUGE THEORY OF NODAL SPINONS AND ANTIFERROMAGNETIC LONG-RANGE ORDER

2006 ◽  
Vol 21 (39) ◽  
pp. 2947-2960
Author(s):  
IKUO ICHINOSE
Keyword(s):  
Phase Transition ◽  
Gauge Theory ◽  
Strong Coupling ◽  
Long Range ◽  
Chemical Potential ◽  
Quantum Critical Point ◽  
Range Order ◽  
Effective Theory ◽  
Long Range Order ◽  
Density Region

In this paper we shall study a gauge theory of nodal spinons which appears as a low-energy effective theory for antiferromagnetic (AF) Heisenberg models. In most of the studies on the nodal spinons given so far, the gauge interaction between spinons was assumed weak and nonperturbative effects like instantons and vortices were ignored. In this paper, we shall study strong-coupling gauge theory of nodal spinons and reveal its nontrivial phase structure. To this end, we employ recently developed lattice gauge theory techniques for studying finite-temperature and finite-density gauge theory. At low temperature and low spinon-density region, an AF long-range order exists. As temperature and/or density of spinons increase, a phase transition to nonmagnetic phase takes place. Order of the phase transition is of second (first) order for low (high) density region of spinons. At a quantum critical point at vanishing temperature T = 0, abrupt change of spinon density occurs as a function of the chemical potential. Implications of the results to the heavy-fermion materials and the high-T c cuprates are discussed.

LONG RANGE ORDER IN THE BLUME-EMERY-GRIFFITHS MODEL

1991 ◽  
Vol 05 (23) ◽  
pp. 1583-1590
Author(s):  
M. CORGINI
Keyword(s):  
Phase Transition ◽  
Long Range ◽  
Order Phase Transition ◽  
Range Order ◽  
Long Range Order ◽  
First Order ◽  
First Order Phase Transition ◽  
Infrared Bounds ◽  
First Order Phase

Using the Infrared Bounds method it ws demonstrated that a first order phase transition takes place in the m-dimensional (m≥3) Blume-Emery-Griffiths model.

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