Phase transitions in the decomposition of $SU(N)$ representations

Abstract

We study the multiplicity of irreducible representations in the decomposition of $n$ fundamentals of $SU(N)$ weighted by a power of their dimension in the large $n$ and large $N$ double scaling limit. A nontrivial scaling is obtained by keeping $n/N^2$ fixed, which plays the role of an order parameter. We find that the system generically undergoes a fourth order phase transition in this parameter, from a dense phase to a dilute phase. The transition is enhanced to third order for the unweighted multiplicity, and disappears altogether when weighting with the first power of the dimension. This corresponds to the infinite temperature partition function of non-Abelian ferromagnets, and the results should be relevant to the thermodynamic limit of such ferromagnets at high temperatures.

arXiv commentVersion published in NPB, extra references; 35 pages, 6 figures

References in corpus (21)

• The Hagedorn Transition, Deconfinement and N=4 SYM Theory
• Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Ultracold Gases of Ytterbium: Ferromagnetism and Mott States in an SU(6) Fermi System
• A Matrix Model for the Two Dimensional Black Hole
• Physics and Mathematics of Calogero particles
• Phases of one-dimensional SU(N) cold atomic Fermi gases --from molecular Luttinger liquids to topological phases
• Exact Spectrum of SU(n) Spin Chain with Inverse-Square Exchange
• Equivalence of Two Dimensional QCD and the $c=1$ Matrix Model
• On free energy of 2-d black hole in bosonic string theory
• Quantum and Thermal Phase Transitions of the Triangular SU(3) Heisenberg Model under Magnetic Fields
• Anatomy of Deconfinement
• Nagaoka states in the SU($n$) Hubbard model
• Exact Results on Itinerant Ferromagnetism and the 15-puzzle Problem
• Structure of Spin Correlations in High Temperature SU($N$) Quantum Magnets
• Ferromagnetism in $d$-dimensional SU($n$) Hubbard models with nearly flat bands
• Deconfinement transition as black hole formation by the condensation of QCD strings
• Microstates of a $2d$ Black Hole in string theory
• Ferromagnetism in the SU(N) Kondo lattice model -- SU(N) double exchange and supersymmetry
• Linear Flavor-Wave Analysis of SU(4)-Symmetric Tetramer Model with Population Imbalance
• Composing arbitrarily many $SU(N)$ fundamentals

Cited by in corpus (2)

• Nonabelian ferromagnets with three-body interactions
• Adjoint ferromagnets