2009/02/26 by C. M. S. da Conceição, E. C. Marino · 1 citation
Physics and Astronomy · #Advanced Condensed Matter Physics #Antiferromagnetism #Condensed matter physics #Heisenberg model #Ising model #Mathematical physics #Phase (matter) #Phase diagram #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Quantum phase transition #Spin glass #Theoretical and Computational Physics #cond-mat.str-el #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2009.02.023
To appear in Nucl. Phys B [FS], 16 pages, 6 figures
openalex publication_date 2009/02/26 · arxiv created 2009/03/02 · arxiv updated 2015/05/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the quenched disordered magnetic system, which is obtained from the 2D SO(3) quantum Heisenberg model, on a square lattice, with nearest neighbors interaction, by taking a Gaussian random distribution of couplings centered in an antiferromagnetic coupling, J¯>0 and with a width ΔJ. Using coherent spin states we can integrate over the random variables and map the system onto a field theory, which is a generalization of the SO(3) nonlinear sigma model with different flavors corresponding to the replicas, coupling parameter proportional to J¯ and having a quartic spin interaction proportional to the disorder (ΔJ). After deriving the CP1 version of the system, we perform a calculation of the free energy density in the limit of zero replicas, which fully includes the quantum fluctuations of the CP1 fields zi. We, thereby obtain the phase diagram of the system in terms of (T,J¯,ΔJ). This presents an ordered antiferromagnetic (AF) phase, a paramagnetic (PM) phase and a spin-glass (SG) phase. A critical curve separating the PM and SG phases ends at a quantum critical point located between the AF and SG phases, at T=0. The Edwards–Anderson order parameter, as well as the magnetic susceptibilities are explicitly obtained in each of the three phases as a function of the three control parameters. The magnetic susceptibilities show a Curie-type behavior at high temperatures and exhibit a clear cusp, characteristic of the SG transition, at the transition line. The thermodynamic stability of the phases is investigated by a careful analysis of the Hessian matrix of the free energy. We show that all principal minors of the Hessian are positive in the limit of zero replicas, implying in particular that the SG phase is stable.