Frustrated phase transitions

Geometric Spin Frustration and Spin-Phase Transitions... 

Figure 9. Model for understanding the commensurate-incommensurate phase transition. The Cu(A) system is ordered. The Cu(B) system is disordered because of the frustration caused by the geometrically competing interaction. The molecular field from the Cu(B) system disturbs the order in the Cu(A) system.

Abstract Existing data on 63Cu-nuclear spin relaxation reveal two independent relaxation processes the one that is temperature independent we link to incommensurate peaks seen by neutrons, while the "universal temperature dependent contribution coincides with 1/6371 (1/ ) for two-chain YBCO 124. We argue that this new result substitutes for a "pseudogap regime in a broad class of high-Tc cuprates and stems from the 1st order phase transition that starts well above the superconductivity Tc but becomes frustrated because of broken electroneutrality in the CuC>2 plane. 

We attempt below to put the results in the context of a phase separation [4]. The decomposition of l/63l/ i(T, x) into two terms, as it will be discussed below in more details, manifests itself in a broad temperature interval above Tc. It is limited from above by a T that depends on the concentration, x. We consider T defined in this way as a temperature of a 1st order phase transition, which, however, cannot complete itself in spatial coexistence of two phases because of the electroneutrality condition [5]. It was already argued in [4] that such a frustrated 1st order phase transition may actually bear a dynamical character. The fact that a single resonant frequency for the 63Cu nuclear spin is observed in the NMR experiments, confirms this suggestion. Although in what follows, we use the notions of the lattice model [4, 5], even purely electronic models [6-9] for cuprates may reveal a tendency to phase separation. 

Rb and 1H SLR rate as a function of temperature is a very important parameter which shows the suppression of phase transition and reveals the frustration in the mixed system. Temperature dependence of Ti in any ordered system can be described by the well known Bloembergen-Purcell-Pound (BPP) type expression. However, disordered systems show deviations from BPP behaviour, showing a broad distribution of relaxation times. The magnetization recovery shows a stretched exponential recovery of magnetization following M(t)=Mo(1 — 2 exp (— r/Ti) ) where a is the stretched exponent. 

A transition from fluid to solid in the mechanical response accompanying the frustrated fluid-solid phase transition,... 

ZnCr204 shows typical signs of GFM behavior with c = -330 K but no sign of magnetic order until Tn = 12.5 K, a frustration index The magnetic phase transition is... 

In this chapter we will review recent developments in the simulation of lattice (and continuum) models by classical and quantum Monte Carlo simulations. Unbiased numerical methods are required to obtain reliable results for classical and quantum lattice model when interactions or fluctuations are strong, especially in the vicinity of phase transitions, in frustrated models and in systems where quantum effects are important. For classical systems, molecular dynamics or the Monte Carlo method are the methods of choice since they can treat large systems. 

While cluster updates can solve critical slowing down at second order phase transitions they are usually inefficient at first order phase transitions and in frustrated systems. Let us consider a first order phase transition, such as in a two-dimensional q -state Potts model with Hamilton function... 

The simulation of frustrated systems suffers from a similar tunneling problem as the simulation of first order phase transitions local minima in energy space are separated by barriers that grow with system size. While the multicanonical or optimized ensembles do not help with the NP-hard problems faced by spin glasses, they are efEcient in speeding up simulations of frustrated magnets without disorder. 

It is straightforward to imagine protein conformational changes that couple to the stress of a frustrated monolayer elastic curvature. The experiments described in the preceding sections demonstrate that there is an energetically significant elastic stress locked into the leaflets of a lamellar bilayer near to a lamellar-nonlamellar phase transition. Experimentally, bilayers near to a lamellar-nonlamellar transition means that relatively... 

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