We develop an efficient algorithmic approach for approximate counting and sampling in the low-temperature regime of a broad class of statistical physics models on finite subsets of the lattice $\mathbb Z^d$ and on the torus $(\mathbb Z/n \mathbb Z)^d$. Our approach is based on combining contour representations from Pirogov-Sinai theory with Barvinok's approach to approximate counting using truncated Taylor series. Some consequences of our main results include an FPTAS for approximating the partition function of the hard-core model at sufficiently high fugacity on subsets of $\mathbb Z^d$ with appropriate boundary conditions and an efficient sampling algorithm for the ferromagnetic Potts model on the discrete torus $(\mathbb Z/n \mathbb Z)^d$ at sufficiently low temperature.

翻译：我们针对广泛一类统计物理模型在格点ℤ^d的有限子集及环面(ℤ/nℤ)^d上的低温区域，开发了一种高效的近似计数与采样算法方法。该方法融合了皮罗戈夫-西奈理论中的等高线表示与巴维诺克利用截断泰勒级数进行近似计数的技术。主要结果的应用包括：在适当边界条件下，对ℤ^d子集上高逸度硬核模型的配分函数近似给出全多项式时间近似方案(FPTAS)；以及针对离散环面(ℤ/nℤ)^d上充分低温下的铁磁波茨模型，给出高效采样算法。