Phase diagrams of the multitrace quartic matrix models of noncommutativeΦ4theory

Abstract

We report a direct and robust calculation, free from ergodic problems, of the nonuniform-to-uniform (stripe) transition line of noncommutative Φ 4 2 by means of an exact Metropolis algorithm applied to the first non-trivial multitrace correction of this theory on the fuzzy sphere. In fact, we reconstruct the entire phase diagram including the Ising, matrix and stripe boundaries together with the triple point. We also report that the measured critical exponents of the Ising transition line agrees with the Onsager values in two dimensions. The triple point is identified as a termination point of the one-cut-totwo-cut transition line and is located at (b,c) = (−1.55, 0.4) which compares favorably with previous Monte Carlo estimate. *

Lectures on Matrix Field Theory

“…Furthermore, multitrace matrix models do not come with a Laplacian, yet one can attach to them an emergent geometry if the uniform ordered phase is sustained. See for example [169,170]. Also, it is quite obvious that these multitrace matrix models lend themselves quite naturally to the matrix renormalization group approach of [163][164][165][166].…”

“…See next chapter. The phase diagrams of various multitrace models of noncommutative phi-four on the fuzzy sphere are reported in [169,170]. They are shown on figure (4.4).…”

“…The algorithm of [147] is the only known method, until [153,169,170], which is 1 Not available on the ArXiv.…”

Triple point of a scalar field theory on a fuzzy sphere

“…Noncommutative (or fuzzy) spaces and field theories on them have been studied extensively both analytically [10][11][12][13][14][15][16][17][18][19][20][21][22][23] and numerically [24,[27][28][29][30][31][32]. A good example is the scalar field theory with a quartic potential on a fuzzy sphere, i.e.…”

The numerical approach to quantum field theory in a noncommutative space

“…[52]), in a tridimensional version of the model [53,54], at finite temperature [55], in a multi-trace formulation [56,57], et c. 1 The results of these numerical simulations can be compared with several analytical studies, including refs. [5,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76].…”