(March 27, 2025 16:30) Race Development for the Quantum Ising Model (Mathematical Physics Seminar)
Date : Thursday, March 27, 2025
Time : From 16:30 to 18:00
Place: W1-C-616
Speaker : KAMIJIMA Yoshinori（Toyo University）
Summary
Abstract: One of the models of ferromagnets is the Ising model. It is known to exhibit critical phenomena, such as the divergence of susceptibility in a power-law manner, by changing the temperature parameter. The power-law exponent, called the critical exponent, is expected to have universality, and in particular, in higher dimensions, the critical exponent of the Ising model matches that of the corresponding non-interacting model. Meanwhile, the model with a transverse magnetic field applied to the Ising model is called the quantum Ising model. In the classical Ising model, the Hamiltonian is given only by the Pauli matrix in the z-axis direction, whereas in the quantum Ising model, it is given by the Pauli matrices in both the z-axis and x-axis directions, resulting in quantum effects due to their non-commutativity. Due to quantum effects, phase transitions occur not only by changing the temperature but also by changing the strength of the transverse magnetic field. In this talk, assuming reflection positivity, we show that the critical exponent of susceptibility for the quantum Ising model in higher dimensions is 1. Additionally, as an attempt to demonstrate this without relying on reflection positivity, we aim to derive race development. We will also discuss the current research results. This research is a joint study with SAKAI Akira (Hokkaido University).
(https://www.math.kyushu-u.ac.jp/activities/13279/)