Phase transition in $SU(N)$ symmetric models for the adjoint field φ in the case of arbitrary N is investigated. We examine the fluctuation-induced symmetry breaking from the point of view of the ferromagnetic phase transition in the large spin Fermi system, where the order parameter $〈\mathrm{\phi }〉$ occurs discontinuously for $N\ge 4$. The free energies of the systems are analyzed within both ε-expansion and the functional renormalization group.

中文翻译：

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关于SU（N）矩阵模型的一阶相变。

相变 $\mathrm{小号}ü（ñ）$研究了任意N情况下伴随场φ的对称模型。我们从大型自旋费米系统中的铁磁相变的角度研究了波动引起的对称性破坏，其中阶数参数$〈\mathrm{\phi }〉$ 不连续发生 $ñ\ge 4$。系统的自由能在ε展开和功能重整化组中进行分析。