Abstract
Motivated by the rich phase diagram of the high-temperature superconductors, we introduce a pseudospin model with three state variables which can be interpreted as two states (spin ±1/2) particles and holes. The Hamiltonian has a term which favors antiferromagnetism and an additional competing interaction which favors bonding between pairs of antiparallel spins mediated by holes. For low concentration of holes the dominant interaction between particles has antiferromagnetic character, leading to an antiferromagnetic phase in the temperature-hole concentration phase diagram, qualitatively similar to the antiferromagnetic phase of doped Mott insulators. For growing concentration of holes antiferromagnetic order is weakened and a phase with a different kind of order mediated by holes appears. This last phase has the form of a dome in the T-hole concentration plane. The whole phase diagram resembles those of some families of high-T_{c} superconductors. We compute the phase diagram in the mean-field approximation and characterize the different phase transitions through Monte Carlo simulations.
Highlights
One of the frontiers of modern condensed matter physics is the description of phase transitions in complex many body systems that challenge the well known theories of classical fluids or the well established quantum theories of Fermi or Bose liquids
When two or more competing interactions are present, usually strong correlations play a significant role in the physics at low temperatures and the phase diagram can show a rich variety of different phases, with different symmetries and thermodynamic properties
We introduced an effective lattice-gas model of spin 1/2 particles doped with holes, to analyze the effect of the competition between an exchange antiferromagnetic interaction and a pairing interaction mediated by holes
Summary
One of the frontiers of modern condensed matter physics is the description of phase transitions in complex many body systems that challenge the well known theories of classical fluids or the well established quantum theories of Fermi or Bose liquids. The common presence of quenched disorder in the samples leads to freezing of degrees of freedom and spin glass like behavior in some cases From this crude exposition of the thermal phenomenology of high Tc superconductors one can immediately conclude that obtaining a complete phase diagram is a formidable task. Extensions of the BEG model has been proposed to describe some aspects of superconductivity [23] With this in mind and motivated by the rich complexity of the phase diagram of high Tc superconductors, in this paper we introduce a very simplified model which captures the topology of the antiferromagnetic and superconductor phases of those systems. The present model is clearly too simplified to describe the complex physics of the cuprates or iron based superconductors, we think it can be useful to think on the universal or robust thermal properties which can lead to the particular phase diagrams of such systems
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