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Volumn 67, Issue 5, 2003, Pages

Multicritical phenomena in (formula presented)-symmetric theories

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[No Author keywords available]

Indexed keywords


EID: 85038953103     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.67.054505     Document Type: Article
Times cited : (27)

References (89)
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    • A different claim has been recently reported in Ref. 35, starting from the projected SO(5) model. Using the typical values of the parameters characterizing the breaking of the O(5) symmetry and the crossover exponent at the O(5) FP, they argued that crossover effects from the O(5) behavior should be observable only for (Formula presented) i.e., in an extremely small interval of reduced temperatures. This fact led the authors to conclude that the multicritical behavior is effectively dominated by the O(5) FP and that it is practically impossible to observe both experimentally and numerically the flow out of the symmetric O(5) FP. In order to obtain the above-reported estimate of (Formula presented) they computed the crossover exponent from its (Formula presented) approximation (Ref. 3,), i.e., (Formula presented) and (Formula presented) thus (Formula presented) setting (Formula presented) Unfortunately, the actual value of (Formula presented) is much larger: (Formula presented) Taking for granted the arguments leading to the estimate (Formula presented) one can easily see that, using the actual value of (Formula presented) the crossover reduced temperature (Formula presented) would change from (Formula presented) to (Formula presented) where (Formula presented) Taking into account that this is a very rough estimate, which may easily miss one order of magnitude, one cannot exclude the possibility of observing experimentally and numerically the unstable flow towards the eventual critical behavior, even in systems with a moderately small breaking of the O(5) symmetry at the multicritical point
    • A different claim has been recently reported in Ref. 35, starting from the projected SO(5) model. Using the typical values of the parameters characterizing the breaking of the O(5) symmetry and the crossover exponent at the O(5) FP, they argued that crossover effects from the O(5) behavior should be observable only for (Formula presented) i.e., in an extremely small interval of reduced temperatures. This fact led the authors to conclude that the multicritical behavior is effectively dominated by the O(5) FP and that it is practically impossible to observe both experimentally and numerically the flow out of the symmetric O(5) FP. In order to obtain the above-reported estimate of (Formula presented) they computed the crossover exponent from its (Formula presented) approximation (Ref. 3,), i.e., (Formula presented) and (Formula presented) thus (Formula presented) setting (Formula presented) Unfortunately, the actual value of (Formula presented) is much larger: (Formula presented) Taking for granted the arguments leading to the estimate (Formula presented) one can easily see that, using the actual value of (Formula presented) the crossover reduced temperature (Formula presented) would change from (Formula presented) to (Formula presented) where (Formula presented) Taking into account that this is a very rough estimate, which may easily miss one order of magnitude, one cannot exclude the possibility of observing experimentally and numerically the unstable flow towards the eventual critical behavior, even in systems with a moderately small breaking of the O(5) symmetry at the multicritical point.
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    • Note that in two dimensions the (Formula presented) fixed point is still stable for (Formula presented) since the spin-(Formula presented) perturbation is irrelevant in this case [R.A. Pelcovits and D.R. Nelson, Phys. Lett. 57A, 23 (1976)]. For (Formula presented) the cubic and higher-order spin perturbations are marginal.
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    • In order to obtain field-theory estimates of the critical exponents for the three-dimensional O(5) universality class, we analyzed the available six-loop fixed-dimension expansions reported in S.A. Antonenko and A.I. Sokolov, Phys. Rev. E 51, 1894 (1995) and the five-loop (Formula presented) expansions reported in Refs. 39, and 40,. Using the conformal mapping method (Ref. 42,), we obtained (Formula presented) (Formula presented) from the fixed-dimension expansion and (Formula presented) (Formula presented) from the (Formula presented) expansion.
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    • The same analysis can be performed in two dimensions: the DFP turns out to be stable for (Formula presented) (Formula presented) and (Formula presented) (Formula presented)
    • The same analysis can be performed in two dimensions: the DFP turns out to be stable for (Formula presented) (Formula presented) and (Formula presented) (Formula presented)
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    • The projected SO(5) model (Ref. 6,) was introduced to overcome some inconsistencies between the original SO(5) theory and the physics of the Mott insulating gap
    • The projected SO(5) model (Ref. 6,) was introduced to overcome some inconsistencies between the original SO(5) theory and the physics of the Mott insulating gap.


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