Browsing by Author "Suthat Yoksan"

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    Elementary excitation of the bimodal ising spin glass on a square lattice
    (Mahidol University. Mahidol University Library and Knowledge Center, 2023) Noparit Jinuntuya; Poulter, Julian; Tang, I. Ming; Suthat Yoksan
    In this thesis we investigate the energy gap of the bimodal Ising spin glass model on a square lattice. We study systems with periodic boundary conditions in one direction, embedded in an infinite ferromagnetic nest in the second direction. The Pfaffian method and degenerate state perturbation theory are used to calculate the degeneracies of the low-lying states. The existence of an energy state can be determined from the non-zero value of its degeneracy. We find that energy gaps depend strongly on the defect concentration and the system size. In the ferromagnetic phase, the energy gap is 4J, no matter what the system size is. In the spin glass phase, on the contrary, the energy gap is 2J when the system size L is odd, while it is 4J when L is even. For the system with odd L, finite size scaling analysis suggests to us that there is a sharp transition concentration pc = 0.1045(11) where 2J excitations start to exist. This value of pc agrees well with the ferromagnetic-spin glass transition concentration found in the literature. We find that the 2J excitations are involved with spins across the system. We expect that these spanning excitations are a characteristic of the spin glass phase. We also investigate the distributions of the degeneracies of the 2J and 4J states, and find that they develop fat tails when L is increasing. Sample-tosample fluctuations of the distributions suggest to us that we cannot expect that the first excited states will dominate the low temperature heat capacity. Elementary excitations of the spin glass model are not represented by the energy gap, and should involve many (if not all) excited states.