Ultrasonic Velocity and Modified Critical Behaviour in the Random-Field Ising System DyAsxV1-xO4
Recently there has been considerable interest in the effects of random fields on Ising phase transitions [1–14]. In their pioneering paper, IMRY and MA  were the first to suggest that random fields destroy long-range order in Ising systems when the dimensionality d is less than dℓ = 2 and that the phase transition which occurs for d > dℓ is characterized by drastically different critical behaviour. Subsequent analyses of the random-field Ising model (RFIM) have resulted in many debates on both of these issues . While it is now generally agreed that the lower critical dimenionality dℓ is indeed equal to 2 , there is still controversy concerning the correct description of the critical properties. It has been suggested [4–6] that the modified critical behaviour of random-field systems can be explained in terms of a reduction in the effective dimensionality, whereby the random-field exponents in d dimensions are equal to those for zero random field in d̄ = d — δ dimensions. Evidence for a dimensionality shift δ of 1 has come from numerical simulations  of the RFIM and from experiments  on randomly-diluted antiferromagnets in a uniform field, a system believed to be equivalent to a pure ferromagnet in a random field .
KeywordsZircon Attenuation Acoustics
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- 18.R.L. Melcher: In Physical Acoustics Vol. 12, ed. by W.P. Mason and R.N. Thurston (Academic, New York 1976)Google Scholar