Institute of Physics ⌽ DEUTSCHE PHYSIKALISCHE GESELLSCHAFT the presence of the SRO phase. An SRO phase is found to have lower energy than either the FM or AF phases for 0.26 p < 1. Phase separation (PS) disappears as J H → 0 but appears for any nonzero coupling. For fillings near p = 1, PS occurs between an AF with p = 1 and either an SRO or a FM phase. The stability of an SRO state at T = 0 can be understood by examining the interacting density-ofstates, which is gapped for any nonzero J H in an AF but only when J H exceeds a critical value in an SRO state. Institute of Physics ⌽ DEUTSCHE PHYSIKALISCHE GESELLSCHAFT Figure 1. A Bethe lattice with z c = 4 nearest neighbours. As shown, the Bethe lattice may be partitioned into A and B sublattices, denoted by the blue and red dots. and antiferromagnetic (AF) phases are magnetically frustrated by a Ruderman-Kittel-Kasuya-Yosida (RKKY)-like interaction between the local moments [7]. This paper uses dynamical mean-field theory (DMFT) to evaluate the magnetic instabilities and T = 0 phase diagram of the DE model. Developed in the late 1980s by Müller-Hartmann [8] and Metzner and Vollhardt [9], DMFT exploits the momentum-independence of the self-energy in infinite dimensions, where DMFT becomes formally exact. Even in three dimensions, DMFT is believed to capture the physics of correlated systems including the narrowing of electron bands and the Mott-Hubbard transition [10]. Although DMFT has been widely applied to the DE model [4, 5], [11]-[18], until now there has been no complete treatment of the phase instabilities and T = 0 phase diagram of the DE model for arbitrary J H and p.We shall study a system with a bare semicircular density-of-states (DOS) given by N 0 (ω) = (8/πW 2 )Re W 2 /4 − ω 2 . In real space, this DOS belongs to an infinite-dimensional Bethe lattice or an infinite Cayley tree with no closed loops [19]. A finite-dimensional Bethe lattice with coordination number z c = 4 is sketched in figure 1. Although the Bethe lattice lacks translational symmetry, it is quite convenient for calculations. As shown in figure 1, the Bethe lattice can be partitioned into A and B sublattices so that both FM and AF long-range orders are possible. Due to the bounds ±W/2, the DOS of the Bethe lattice more closely resembles the DOS of two-and three-dimensional systems than does the unbounded DOS of the hypercubic lattice. Indeed, pathological results have been obtained on a hypercubic lattice due to the asymptotic freedom of the quasiparticles in the tails of the Gaussian DOS [16]. As we shall see, the Bethe lattice also has the advantage that analytic results are possible in the limit of small J H , precisely the regime where controversies persist.The high-temperature, non-magnetic (NM) phases of the Heisenberg and DE models have a correlation length ξ that vanishes as z c → ∞. By contrast, the short-range ordered (SRO) states introduced in an earlier paper [20] possess some of the same characteristics as spin glasses: local magnetic order and exponentially decaying magnet...
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