Spin-Chirality Decoupling in the One-Dimensional Heisenberg Spin Glass with Long-Range Power-Law Interactions

Abstract

We study the issue of the spin-chirality decoupling or coupling in the ordering of the Heisenberg spin glass by performing large-scale Monte Carlo simulations on a one-dimensional Heisenberg spin-glass model with a long-range power-law interaction up to large system sizes. We find that the spin-chirality decoupling occurs for an intermediate range of the power-law exponent. Implications to the corresponding d-dimensional short-range model are discussed.

Phase transitions in the one-dimensional long-range diluted Heisenberg spin glass

“…Again, the inset shows log-log fits assuming that the transition temperature, T CG in this case, is zero. The fit is satisfactory and indicates that we do not find a finite value for T CG at σ = 1, in contrast to the claim of Viet and Kawamura [20]. Figure 14 shows the data for χ SG .…”

“…It is known from the early work of Kotliar et al [3] that σ = 1 is the "lower critical" value σ l , above which there is no spin glass transition. Interestingly, Viet and Kawamura [20] claim that chiral glass ordering persists to slightly larger values of σ. Testing this claim is one of our main motivations for performing simulations at σ = 1.…”

“…Our primary motivation to study the Heisenberg spin glass in one dimension with long-range interactions which fall off with the power of the distance, is to test Kawamura's spin-chirality decoupling scenario in which T CG > T SG , and his subsequent prediction [20] that chiral glass ordering persists for σ > σ l , where σ l = 1 is the "lower critical" value for the spin glass transition, with a finite value of T CG at σ = 1.…”

“…One motivation is that Kawamura [9] proposed that there are two separate transitions in vector spin glasses, a spin glass transition at T = T SG and a "chiral glass transition" at higher temperature T CG , involving a freezing of vortex-like variables called chiralities. While the original scenario had T SG = 0, it now appears that T SG is non-zero in three or more dimensions, but the ques- * Electronic address: peter@physics.ucsc.edu tion of whether T SG < T CG , or whether there is a single transition at which both types of ordering occur, is still open [10][11][12][13][14][15][16][17][18][19][20].…”

Ordering of the Heisenberg spin glass in four dimensions

“…Indeed, several studies both for the Ising and the Heisenberg SGs suggested that the 1D LR SG model with a power-law exponent σ might show the ordering behavior analogous to the d-dimensional SG model with a SR interaction [23][24][25][26][27][28][29][30][31]. Even a simple empirical formula relating σ and d, d = 2/(2σ − 1), was proposed [23], though the relation is only approximate.…”