Analyticity of the partition function for finite quantum systems

Atish Dabholkar A, Upamanyu Moitra

We analyze the one-loop quantum entanglement entropy in ten-dimensional type-II string theory using the orbifold method by analytically continuing in N the genus-one partition function for string orbifolds on R 2 / Z N conical spaces known for all odd integers N > 1 . We show that the tachyonic contributions to the orbifold partition function can be appropriately summed and analytically continued to an expression that is finite in the physical region 0 < N ≤ 1 resulting in a finite and calculable answer for the entanglement entropy. We discuss the implications of the finiteness of the entanglement entropy for the information paradox, quantum gravity, and holography. Published by the American Physical Society 2024

Huzihiro Araki

Ph. Audit

A new matrix product is defined and used in connection with three other well-known matrix products in order to derive analytical solutions of finite three-dimensional Ising systems. As an example, the exact partition function of the periodic anisotropic 2 x 2 x 2 lattice in a field is evaluated from which analytical expressions for the magnetization and the specific heat of this system follow.

Barry Simon A

Bingyu Cui

Petr Dmitrievich Andriushchenko, Konstantin Valentinovich Nefedev

The results of studies of 1D Ising models and Curie-Weiss models partition functions structure are presented in this work. Exact calculation of the partition function using the authors combinatorial approach for such system is discussed. The distribution of the energy levels degeneracy was calculated. Analytical solution for density of states of 1D Ising chain were obtained. Generating functions for these models were obtained. It was suggested that in Curie-Weiss model the transition to a low-energy state occurs without the formation of separation boundaries