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Register a new userDevils Staircase Continuum in the Chiral Clock Spin Glass with Competing Ferromagnetic-Antiferromagnetic and Left-Right Chiral Interactions
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The chiral clock spin-glass model with q=5 states, with both competing ferromagnetic-antiferromagnetic and left-right chiral frustrations, is studied in d=3 spatial dimensions by renormalization-group theory. The global phase diagram is calculated in temperature, antiferromagnetic bond concentration p, random chirality strength, and right-chirality concentration c. The system has a ferromagnetic phase, a multitude of different chiral phases, a chiral spin-glass phase, and a critical (algebraically) ordered phase. The ferromagnetic and chiral phases accumulate at the disordered phase boundary and form a spectrum of devils staircases, where different ordered phases characteristically intercede at all scales of phase-diagram space. Shallow and deep reentrances of the disordered phase, bordered by fragments of regular and temperature-inverted devils staircases, are seen. The extremely rich phase diagrams are presented as continuously and qualitatively changing videos.
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Spin glass (SG) is a typical magnetic system with frozen random spin orientation at low temperatures. The system exhibits rich physical properties, such as infinite number of ground states, memory effect and aging phenomena. There are two main ingredients considered to be pivotal for the existence of SG behavior, namely, frustration and randomness. For the canonical SG system, frustration is led by the presence of competing interaction between ferromagnetic (FM) and antiferromagnetic (AF) couplings. Previously, Bartolozzi {it et al.} [ Phys. Rev. B{bf 73}, 224419 (2006)], reported the SG properties of the AF Ising spins on scale free network (SFN). It is a new type of SG, different from the canonical one which requires the presence of both FM and AF couplings. In this new system, frustration is purely caused by the topological factor and its randomness is related to the irregular connectvity. Recently, Surungan {it et. al.} [Journal of Physics: Conference Series 640, 012001 (2015)] reported SG bahavior of AF Heisenberg model on SFN. We further investigate this type of system by studying an AF Heisenberg model on rewired square lattices. We used Replica Exchange algorithm of Monte Carlo Method and calculated the SG order parameter to search for the existence of SG phase.
Across many scientific and engineering disciplines, it is important to consider how much the output of a given system changes due to perturbations of the input. Here, we study the robustness of the ground states of $pm J$ spin glasses on random graphs to flips of the interactions. For a sparse graph, a dense graph, and the fully connected Sherrington-Kirkpatrick model, we find relatively large sets of interactions that generate the same ground state. These sets can themselves be analyzed as sub-graphs of the interaction domain, and we compute many of their topological properties. In particular, we find that the robustness of these sub-graphs is much higher than one would expect from a random model. Most notably, it scales in the same logarithmic way with the size of the sub-graph as has been found in genotype-phenotype maps for RNA secondary structure folding, protein quaternary structure, gene regulatory networks, as well as for models for genetic programming. The similarity between these disparate systems suggests that this scaling may have a more universal origin.
The devils staircase is a term used to describe surface or an equilibrium phase diagram in which various ordered facets or phases are infinitely closely packed as a function of some model parameter. A classic example is a 1-D Ising model [bak] wherein long-range and short range forces compete, and the periodicity of the gaps between minority species covers all rational values. In many physical cases, crystal growth proceeds by adding surface layers which have the lowest energy, but are then frozen in place. The emerging layered structure is not the thermodynamic ground state, but is uniquely defined by the growth kinetics. It is shown that for such a system, the grown structure tends to the equilibrium ground state via a devils staircase traversing an infinity of intermediate phases. It would be extremely difficult to deduce the simple growth law based on measurement made on such an grown structure.
All higher-spin s >= 1/2 Ising spin glasses are studied by renormalization-group theory in spatial dimension d=3. The s-sequence of global phase diagrams, the chaos Lyapunov exponent, and the spin-glass runaway exponent are calculated. It is found that, in d=3, a finite-temperature spin-glass phase occurs for all spin values, including the continuum limit of s rightarrow infty. The phase diagrams, with increasing spin s, saturate to a limit value. The spin-glass phase, for all s, exhibits chaotic behavior under rescalings, with the calculated Lyapunov exponent of lambda = 1.93 and runaway exponent of y_R=0.24, showing simultaneous strong-chaos and strong-coupling behaviors. The ferromagnetic-spinglass-antiferromagnetic phase transitions occurring around p_t = 0.37 and 0.63 are unaffected by s, confirming the percolative nature of this phase transition.
Spin glasses are a longstanding model for the sluggish dynamics that appears at the glass transition. However, spin glasses differ from structural glasses for a crucial feature: they enjoy a time reversal symmetry. This symmetry can be broken by applying an external magnetic field, but embarrassingly little is known about the critical behaviour of a spin glass in a field. In this context, the space dimension is crucial. Simulations are easier to interpret in a large number of dimensions, but one must work below the upper critical dimension (i.e., in d<6) in order for results to have relevance for experiments. Here we show conclusive evidence for the presence of a phase transition in a four-dimensional spin glass in a field. Two ingredients were crucial for this achievement: massive numerical simulations were carried out on the Janus special-purpose computer, and a new and powerful finite-size scaling method.
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