Some Remarks on Phase Transitions Generated  by the Superposition of Multifractals

H. J. Chen; H. C. Tseng; W. Y. Lai; W. D. Chen

doi:10.1142/s0217979297001441

Some Remarks on Phase Transitions Generated by the Superposition of Multifractals

International Journal of Modern Physics B ◽

10.1142/s0217979297001441 ◽

1997 ◽

Vol 11 (24) ◽

pp. 2961-2974

Author(s):

H. J. Chen ◽

H. C. Tseng ◽

W. Y. Lai ◽

W. D. Chen

Keyword(s):

Phase Transitions ◽

Phase Diagrams ◽

Second Order

Emergence of novel second-order phase transitions by sums of multifractals was found by Radons and Stoop.1,2 Using the same method as Radons and Stoop but different support, we have found that the second-order phase transitions are suppressed.3 In this paper, we continue to extend the method to three multifractals, with the effect of the sums of the three multifractals being the sums of two identical multifractals and those of two different multifractals combined together. We have found that the resulted phase diagrams are more complicated, with second-order phase transitions either partially or completely suppressed.

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Critical behaviors and phase diagrams of the mixed spin-1 and spin-7/2 Blume-Capel (BC) Ising model on the Bethe lattice (BL)

International Journal of Modern Physics B ◽

10.1142/s0217979215501945 ◽

2015 ◽

Vol 29 (28) ◽

pp. 1550194 ◽

Cited By ~ 3

Author(s):

M. Karimou ◽

R. Yessoufou ◽

F. Hontinfinde

Keyword(s):

Phase Transitions ◽

Phase Diagrams ◽

Ground State ◽

Tricritical Point ◽

Bethe Lattice ◽

Second Order ◽

Temperature Phase ◽

First Order ◽

Crystal Fields ◽

Mixed Spin

Using the recursion equations technique, the influences of the single-ion anisotropies or crystal-fields interactions on the magnetic properties of the mixed spin-1 and spin-7/2 Blume-Capel (BC) Ising ferrimagnetic system are studied on the Bethe lattice (BL). The ground-state phase diagram is constructed, the thermal behaviors of the order-parameters and the free-energy are thoroughly investigated in order to characterize the nature of the phase transitions and to obtain the phase transition temperature. Then, the temperature phase diagrams are obtained in the case of equal crystal-field interactions on the ([Formula: see text] and [Formula: see text]) planes when q = 3, 4 and 6 and in the case of unequal crystal-fields interactions on the ([Formula: see text] and [Formula: see text]) and [Formula: see text] and [Formula: see text]) planes for selected values of [Formula: see text] and [Formula: see text] respectively when q = 3. The model shows first-order and second-order phase transitions, and where the lines are connected is the tricritical point. Besides the first-order and second-order phase transitions, the system also exhibits compensation temperatures depending on appropriate values of the crystal-fields interactions.

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