可和变差类双阱型势的零温相图
Zero-temperature phase diagram for double-well type potentials in the summable variation class
摘要：
本文研究了一类长程势在$\{0,1\}$全位移上的Gibbs测度的零温度极限。这些势由Walters引入作为传递算子的自然空间。在我们的例子中，它们是局部常数、Lipschitz连续的，或者更一般地说，是可和变分的。我们假设恰好存在两个基态：不动点$0^\infty$和$1^\infty$。我们充分的特点，在两个基态之间的Peierls障碍，零温度的相图，这样的潜力，也就是说，收敛或发散的吉布斯措施的温度为零的区域。
英文摘要：
We study the zero-temperature limit of the Gibbs measures of a class of long-range potentials on a full shift of two symbols $\{0,1\}$. These potentials were introduced by Walters as a natural space for the transfer operator. In our case, they are locally constant, Lipschitz continuous or, more generally, of summable variation. We assume there exists exactly two ground states: the fixed points $0^\infty$ and $1^\infty$. We fully characterize, in terms of the Peierls barrier between the two ground states, the zero-temperature phase diagram of such potentials, that is, the regions of convergence or divergence of the Gibbs measures as the temperature goes to zero.
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