Study of Critical Phenomena in Low-Dimensional Magnets

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1. Critical phenomena of S=1 bond-altenating chain and analysis of experimental resultsS=1 antiferromagnetic chain has the energy gap. But it was expected that the alternating bond chain may become gapless at some strength of the alternation. We find that Ni(333-tet)(mu-N_3)(ClO_4)is such a chain with bond alternation. We did the Monte Carlo calculation and the exact diagonalization calculation and compared with experimental results by Hagiwara's group. The coincidence is very good.2. Study of spin systems with long range interactionProperties of the system with long-range interaction are quite different from those of systems with short-range interaction. Generally the short-range interacting spin systems have not phase transition in one and two dimensions. We investigated the low-temperature behavior of correlation length and phase transition of the system with long-range interaction using several approximations.3. Universal magnetic scaling function of ferromagnetic Heisenberg chainM … More agnetization curve of ferromagnetic Heisenberg model at low temperature approaches to some universal scaling function regardless to the fact that the system is classical or quantum. M=M<@D20phiM@>D2(<@D7P<@D2z@>D2H(/)T<@D12@>D1@>D7, <@D7P<@D2z@>D2(/)LT@>D7). Here rho<@D2s@>D2 is the stiffness constant, H is magnetic field, T is the temperature, L is the length of the system, M<@D20@>D2 is the saturation magnetization. We got phi<@D2M@>D2 (g, 0) = <@D72(/)3@>D7g - <@D744(/)135@>D7g<@D13@>D1 + <@D7752(/)2835@>D7g<@D15@>D1 - <@D7465704(/)1913625@>D7g<@D17@>D1 + <@D7356656(/)1515591@>D7g<@D19@>D1 - <@D7707126486624(/)3016973334375@>D7g<@D111@>D1 + <@D71126858624(/)4736221875@>D7g<@D113@>D1 - <@D75083735857217648(/)20771861407171875@>D7g<@D115@>D1 + ・・4. Numerical analysis of Anderson transiton in random magnetic fieldWe analyzed the critical exponents of Anderson transition in random magnetic field using the transfer matrix method. We certified the universality of the Anderson transition in the unitary class. Less