We extend results on quadratic pressure and convergence of Gibbs measures from Leplaideur and Watbled (Bull Soc Math France 147(2):197–219, 2019) to some general models for spin spaces. We define the notion of equilibrium state for the quadratic pressure and show that under some conditions on the maxima for some auxiliary function, the Gibbs measure converges to a convex combination of eigen-measures for the Transfer Operator. This extension works for dynamical systems defined by infinite-to-one maps. As an example, we compute the equilibrium for the mean-field XY model as the number of particles goes to $$+\infty $$ + ∞ .

中文翻译：

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遍历理论中一般自旋空间和二次压力的居里-韦斯型模型

我们将 Leplaideur 和 Watbled (Bull Soc Math France 147(2):197–219, 2019) 关于二次压力和 Gibbs 测度收敛的结果扩展到一些自旋空间的一般模型。我们定义了二次压力的平衡状态的概念，并表明在某些辅助函数的最大值的某些条件下，吉布斯测度收敛到传递算子的特征测度的凸组合。此扩展适用于由无限对一映射定义的动态系统。例如，当粒子数量达到 $$+\infty $$ + ∞ 时，我们计算平均场 XY 模型的平衡。