Phase structure of U(N→∞) gauge theory on a two-dimensional lattice for a broad class of variant actions

1983 ◽  
Vol 220 (2) ◽  
pp. 167-184 ◽  
Author(s):  
J. Jurkiewicz ◽  
K. Zalewski
Keyword(s):  
Gauge Theory ◽  
Phase Structure ◽  
Broad Class ◽  
Two Dimensional ◽  
Dimensional Lattice

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

scholarly journals Loop-TNR analysis of CP(1) model with theta term

2018 ◽  
Vol 175 ◽  
pp. 11015
Author(s):  
Hikaru Kawauchi ◽  
Shinji Takeda
Keyword(s):  
Renormalization Group ◽  
Phase Structure ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Tensor Networks ◽  
Tensor Network ◽  
Network Methods ◽  
Renormalization Method ◽  
Future Work

The phase structure of the two dimensional lattice CP(1) model in the presence of the θ term is analyzed by tensor network methods. The tensor renormalization group, which is a standard renormalization method of tensor networks, is used for the regions θ = 0 and θ ≠ 0. Loop-TNR, which is more suitable for the analysis of near criticality, is also implemented for the region θ = 0. The application of Loop-TNR for the region θ ≠ 0 is left for future work.

THE LATTICE ABELIAN CHERN-SIMONS GAUGE THEORY

1991 ◽  
Vol 06 (22) ◽  
pp. 3919-3931 ◽  
Author(s):  
AL. R. KAVALOV ◽  
R.L. MKRTCHYAN
Keyword(s):  
Gauge Theory ◽  
Wilson Loops ◽  
Two Dimensional ◽  
Close Correspondence ◽  
Dimensional Lattice ◽  
Lattice Version ◽  
Continuous Theory ◽  
Statistical Systems ◽  
Chern Simons

Some properties of the previously proposed lattice version of the Abelian Chern-Simons gauge theory are studied. The lattice analog of BF systems is constructed, and the properties of both theories are found to be in close correspondence with those of the continuous theory. The correspondence with two-dimensional lattice statistical systems is established and the lattice origin of the framing of Wilson loops is shown.

Study on bandgap and directional wave propagation of a two-dimensional lattice with nested core

2022 ◽  
Author(s):  
Jiahong Hou ◽  
Zhijun Zhang ◽  
Dong Li
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Group Velocity ◽  
Phase Structure ◽  
Single Phase ◽  
Lattice Structure ◽  
Two Dimensional ◽  
Practical Application ◽  
Dimensional Lattice ◽  
Directional Wave

Abstract This paper proposed a two-dimensional lattice structure with a nested core. The bandgap distribution and the anisotropy of phase velocity and group velocity were studied based on Bloch’s theorem and finite element method. The effects of eccentric ratio (e) and rotation angle (θ) of dual-phase structure on the bandgap distribution were investigated, and the anisotropy was studied via phase velocity and group velocity. The structure of (e) = 0.3 displayed the maximum total bandgap width. With (θ) increasing, the total bandgap widths of structures of different (e) all increased apparently and the low-frequency bandgap properties were improved. The phase velocity and group velocity of (e) = 0 displayed strong anisotropy, and the anisotropy was tuned by tuning (θ). Furthermore, the group velocity of the eighth mode displayed high directional wave propagation. For practical application, a single-phase structure was proposed and analyzed. Through additive manufacturing technology, the single-phase structure was prepared and tested by a low amplitude test setup. The experimental results displayed a good agreement with numerical results which demonstrated high directional propagation. This finding may pave the way for the practical application of the proposed lattice metamaterial in terms of wave filtering.

scholarly journals Multiple phases in a generalized Gross-Witten-Wadia matrix model

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Jorge G. Russo ◽  
Miguel Tierz
Keyword(s):  
Partition Function ◽  
Matrix Models ◽  
Characteristic Polynomial ◽  
Matrix Model ◽  
Phase Structure ◽  
Unitary Matrix ◽  
Two Dimensional ◽  
Toeplitz Determinants ◽  
Dimensional Parameter ◽  
Planar Limit

Abstract We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed Cauchy ensemble. Exact formulas for the partition function and Wilson loops are given in terms of Toeplitz determinants and minors and large N results are obtained by using Szegö theorem with a Fisher-Hartwig singularity. In the large N (planar) limit with two scaled couplings, the theory exhibits a surprisingly intricate phase structure in the two-dimensional parameter space.

scholarly journals Solving puzzles in deformed JT gravity: phase transitions and non-perturbative effects

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Clifford V. Johnson ◽  
Felipe Rosso
Keyword(s):  
Phase Structure ◽  
Scalar Potential ◽  
String Equation ◽  
Two Dimensional ◽  
Leading Order ◽  
Classical Analysis ◽  
First Order ◽  
First Order Phase Transition ◽  
Definition Of ◽  
First Order Phase

Abstract Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.

Sign in / Sign up

Export Citation Format

Share Document