Phase structure of the generalized two-dimensional Yang-Mills theory on sphere

More on Generalized Simplicial Chiral Models

“…[11]- [13] and the phase structure of some of the specific examples has been studied in refs. [14] and [15]. In all the studied cases, it is seen that the models have third-order phase transition, which is the same behavior as YM 2 .…”

Nonequivalent Ensembles for the Mean-Field φ⁶ Spin Model

“…This structure was observed in the study of the quantum mechanics of a single site, three well potential when classical, perturbative and mean field arguments were used and bubble solutions, their relation to the phase transitions and the question of their stability, both relativistically and non-relativistically. In recent years the 6 model and its application in different physical systems including the following problems have been studied extensively: the crossover from a quantum 6 theory to a renormalized two-dimensional classical nonlinear sigma model [1], alpha matter on a lattice [2], first-order electroweak phase transition (EWPT) due to a dimension six operator in the effective Higgs potential [3], first order phase transitions in confined systems [4], effective potential and spontaneous symmetry breaking in the non-commutative 6 model [5], bubble dynamics in quantum phase transitions [6], the canonical transformation and duality in the 6 theory [7], hermitian matrix model 6 for 2D quantum gravity [8], phase structure of the generalized two dimensional Yang-Mills theories on sphere [9], tricritical Ising model near criticality [10], spontaneous symmetry breaking at two Loop in 3D massless scalar electrodynamics [11], Ising model in the ferromagnetic phase [12], statistical mechanics of nonlinear coherent structures and kinks in the 6 model [13], growth kinetics in the 6 N-Component model [14], stability of Q-balls [15], the liquid states of pion condensate and hot pion matter [16], instantons and conformal holography [17], first order phase transitions in superconducting films [18], field theoretic description of ionic crystallization in the restricted primitive mode [19].…”

Large-N Limit of Nonlocal 2d Generalized Yang–mills Theories on Non-Orientable Surface

“…These theories, however, are defined by replacing an arbitrary class function of B instead of tr(B 2 ) [10]. Several aspect of this theories such as, partition function, generating functional and large -N limit on an arbitrary two dimensional orientable and non-orientable surfaces has been discussed in [16][17][18][19][20][21][22]. There is another way to generalize YM 2 and gYM 2 and that is to use a nonlocal action for the auxiliary field, leading to the so-called nonlocal YM 2 (nlYM 2 ) and nonlocal gYM 2 (nlgYM 2 ) theories, respectively [12].…”

“…This introduces a phase transition between these two regime. Some problem has been studied for special cases of YM 2 [17,23], gYM 2 [20,21,22], nlYM 2 [12,14], nlgYM 2 in [13,15] on sphere. In this paper I investigate this problem ( large-N limit) of nlgYM 2 theories on arbitrary non-orientable surface.…”