Smeared spin-flop transition in random antiferromagnetic Ising chain
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RDER, DISORDER, AND PHASE TRANSITION IN CONDENSED SYSTEM
Smeared SpinFlop Transition in Random Antiferromagnetic Ising Chain1 P. N. Timonin Southern Federal University, RostovonDon, 344090 Russia email: [email protected] Received December 7, 2011
Abstract—At T = 0 and in a sufficiently large field, the nearestneighbor antiferromagnetic Ising chain undergoes a firstorder spinflop transition into the ferromagnetic phase. We consider its smearing under the randombond disorder such that all independent random bonds are antiferromagnetic (AF). It is shown that the groundstate thermodynamics of this random AF chain can be described exactly for an arbitrary distribution P(J) of AF bonds. Moreover, the site magnetizations of finite chains can be found analytically in this model. We consider a contin uous P(J) that is zero above some –J1 and behaves near it as (–J1 – J)λ, λ > –1. In this case, the ferromagnetic phase emerges continuously in a field H > Hc = 2J1. At 0 > λ > –1, it has the usual secondorder anomalies near Hc with the critical indices obeying the scaling relation and depending on λ. At λ > 0, higherorder transitions occur (third, fourth, etc.), marked by a divergence of the corresponding nonlinear susceptibilities. In the chains with an even number of spins, the intermediate “bowtie” phase with linearly modulated AF order exists between the AF and ferromagnetic phases at J1 < H < Hc. Its origin can be traced to the infinite correlation length of the degenerate AF phase from which it emerges. This implies the existence of similar inhomogeneous phases with size and formdependent order in a number of other systems with infinite correlation length. The possibility to observe the signs of the “bowtie” phase in lowT neutron diffraction experiments is discussed. DOI: 10.1134/S1063776112110118 1
INTRODUCTION
The influence of quenched disorder on firstorder phase transitions was first described phenomcnologi cally by Imry and Wortis [1], who have shown that “randomtemperature” disorder can diminish or even eliminate jumps of the order parameter and other vari ables at the transition point. Further studies have revealed a relation of such smeared transitions to the randomfield Ising model [2]; it was shown that the smeared transitions can become secondorder ones [3–5] and can transform into a phase coexistence region instead of a sharp transition [6]. Yet our understanding of these smearing phenomena is far from exhaustive. We still have no rigorous criteria to decide which of the known outcomes of the smear ing—softened jumps, phase coexistence region, or a secondorder transition—will be realized and treat this point only qualitatively [7]. For the resulting second order transition, it is not known definitely whether the critical indices are universal or depend on disorder parameters [3–5]. There is also the unexplored possibil ity that the phase coexistence region, lacking first and secondorder transition anomalies, contains higher order anomalies at some point, appropriate for the highero
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