Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
1998-11-30
Phys. Rev. B, vol. 59, 11925-11935 (1999).
Physics
Condensed Matter
Strongly Correlated Electrons
20 pages, 5 figures
Scientific paper
10.1103/PhysRevB.59.11925
We consider here a generalization of the random quantum rotor model in which each rotor is characterized by an M-component vector spin. We focus entirely on the case not considered previously, namely when the distribution of exchange interactions has non-zero mean. Inclusion of non-zero mean permits ferromagnetic and superconducting phases for M=1 and M=2, respectively. We find that quite generally, the Landau theory for this system can be recast as a zero-mean problem in the presence of a magnetic field. Naturally then, we find that a Gabay-Toulouse line exists for $M>1$ when the distribution of exchange interactions has non-zero mean. The solution to the saddle point equations is presented in the vicinity of the bi-critical point characterized by the intersection of the ferromagnetic (M=1) or superconducting (M=2) phase with the paramagnetic and spin glass phases. All transitions are observed to be second order. At zero temperature, we find that the ferromagnetic order parameter is non-analytic in the parameter that controls the paramagnet/ferromagnet transition in the absence of disorder. Also for M=1, we find that replica symmetry breaking is present but vanishes at low temperatures. In addition, at finite temperature, we find that the qualitative features of the phase diagram, for M=1, are {\it identical} to what is observed experimentally in the random magnetic alloy $LiHo_xY_{1-x}F_4$.
Dalidovich Denis
Phillips Philip
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