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PRODID:-//prob.tw//NTU Seminars V2//EN
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UID:2025-09-09-yoshinori-kamijima-lace-expansion-for-the-quantum-ising-model@seminars.prob.tw
DTSTAMP:20261014T103918Z
DTSTART:20250909T073000Z
DTEND:20250909T083000Z
SUMMARY:Lace expansion for the quantum Ising model
DESCRIPTION:Yoshinori Kamijima (上島芳倫)\nThe lace expansion is one of the powerful tools for investigating critical phenomena.  It has succeeded in obtaining asymptotic expansions for the critical point in several models\, e.g.\, the self-avoiding walk\, ordinary/oriented percolation\, the contact process\, etc.  One of our aims is to obtain such an asymptotic expansion for the quantum Ising model\, which is one of the models of ferromagnetism.  In this model\, Spin configurations are randomly realized by the Hamiltonian operator (energy)\, which involves the z-axis and x-axis Pauli matrices.  In other words\, the quantum Ising model is defined by applying a transverse field to the classical Ising model.  Due to the transverse field\, the quantum Ising model exhibits a different type of phase transition from the classical case.\n\nIn this talk\, I will show the derivation of a lace expansion for the quantum Ising model and upper bounds on the expansion coefficients.  The derivation is based on the random current representation [Björnberg and Grimmett (2009) <i>J. Stat. Phys.</i>] [Crawford and Ioffe (2010) <i>Commun. Math. Phys.</i>] on space-time.  This representation provides the connectivity between two vertices in space-time\, which is similar to percolation models.  It helps us to derive the lace expansion.\n\nThis talk is based on joint work with Akira Sakai (Hokkaido University\, Japan).
LOCATION:台大次震宇宙館 505 室
URL:http://127.0.0.1:8123/?event=2025-09-09-yoshinori-kamijima-lace-expansion-for-the-quantum-ising-model
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