PhD Dissertation: Tolga Çağlar

PhD Dissertation: Tolga Çağlar

CHIRAL SPIN GLASSES, CONTINUUM OF DEVIL’S STAIRCASES, AND THRESHOLDED ROUGHENING FROM FROZEN IMPURITIES

 

 

Tolga Çağlar
Physics, PhD Dissertation, 2017

 

Thesis Jury

Prof. A. Nihat Berker (Thesis Advisor), Prof. Sondan Durukanoğlu Feyiz,

Asst. Prof. Kamer Kaya, Prof. Haluk Özbek, Prof. Mehran Kardar

 

 

Date & Time: June 22nd, 2017 –  3:30 PM

Place: FENS G029

Keywords : Quenched random systems, renormalization-group theory, mean-field theory, phase diagrams, interface roughening, devil’s staircases

 

Abstract

 

The roughening phase diagram of the three-dimensional Ising model with uniaxially anisotropic interactions is calculated for the entire range of anisotropy, using hard-spin mean-field theory. Quenched random pinning centers and missing bonds on the interface of isotropic and anisotropic Ising models show domain boundary roughening that exhibits consecutive thresholding transitions as a function of interaction anisotropy. Quenched random chirality is introduced and investigated using renormalization-group theory for three examples: The global phase diagram of 3−state chiral Potts spin glass with competing left-right chiral interactions is obtained for chirality concentration, chirality breaking concentration and temperature, showing a new spin-glass phase. An unusual fibrous patchwork of microreentrances of all four (ferromagnetic, left chiral, right chiral, chiral spin glass) ordered phases is seen. The spin-glass phase boundary to disordered phase shows, unusually, more chaotic behavior than the chiral spin-glass phase itself. The q−state chiral clock double spin-glass model has competing left-right chiral and ferromagnetic-antiferromagnetic interactions. The global phase diagram is obtained for antiferromagnetic bond concentration, chirality-breaking concentration, random chirality strength, and temperature. The global phase diagram for q = 5 includes a ferromagnetic, a multitude of chiral phases with different pitches, a chiral spin glass, an algebraically ordered critical phases. The ferromagnetic and chiral phases intercede with each other to form a widely varying continuum of Devil’s staircase structures. The global phase diagram for q = 4 shows, four different spin-glass phases, including conventional, chiral, and quadrupolar spin-glass phases, and phase transitions between spin-glass phases. Chaotic behaviors are measured through Lyapunov exponents.