The critical properties of the two-dimensional xy model

Kosterlitz, J

doi:10.1088/0022-3719/7/6/005

Cited by 2,842 publications

(1,826 citation statements)

References 11 publications

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“…Such observations are, however, consistent with gradual decrease of the grain boundary step free energy with temperature as predicted and observed for surface 37,40,44,[47][48][49][50][51] and the transition temperatures varying among the grain boundaries.…”

Section: Resultssupporting

confidence: 89%

Temperature Dependence of Grain Boundary Structure and Grain Growth in Bulk Silicon-Iron.

Choi

Yoon

2003

ISIJ International

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Grain boundary shapes and grain growth in bulk 2.61 wt% silicon-iron have been studied by heat-treating at temperatures between 700 and 1 200°C. Initial microstructure with fairly uniform fine grains has been obtained by recrystallization at 800°C for 5 min after deformation. When subsequently heat-treated at 700 and 800°C, a fraction of the grain boundaries have hill-and-valley shapes with several facet planes or kinks. Some of these facet boundary segments are expected to be singular. Abnormal grain growth occurs at 700 and 800°C and is attributed to step growth of the boundaries. When heat-treated at 1 000°C, all grain boundaries are defaceted with smoothly curved shapes, indicating that they are atomically rough. At temperatures above 1 000°C, normal grain growth occurs, because the rough grain boundaries move continuously. This correlation between grain boundary structure and grain growth is consistent with the earlier observations in other metals and oxides. It is thus shown that the abnormal grain growth in this alloy occurs at low temperatures because of the singular grain boundary structure.KEY WORDS: silicon-iron; silicon-steel; abnormal grain growth; grain boundary faceting; singular grain boundary.ing along the grain boundaries using an image analysis program. For the specimens with fine grains, about 500-2 000 grains were measured, and for those with large grains, about 100-300 grains were measured. The grain boundary shapes were also examined in a transmission electron microscope (TEM). Results and DiscussionWet chemical analysis of the heat-treated bar showed that the Si content was 2.61 wt% and the major impurities were P (0.015 wt%), Ni (0.06 wt%), and Cr (0.01 wt%). The C, Mn, and S contents were about 0.005 wt%. The specimens heat-treated at 800°C for 5 min after compressing to 66.7 % in height had typical primary recrystallization structures with fine grains of 8.7 mm in average radius as shown in Fig. 1. The X-ray pole figure and electron back-scattered pattern (EBSP) analysis of these specimens did not show any macroscopic or microscopic texture. Figure 1 is the initial microstructure for all subsequent heat-treatments at various temperatures to observe the grain growth behavior.The grain growth during the heat-treatment at 600°C was very slow. After 250 h at 600°C, the grains were only slightly larger than those shown in Fig. 1. During the heattreatment at 700°C, typical AGG behavior was observed as shown in the microstructures of Fig. 2, and grain size distributions in Fig. 3. After 3 h, some large grains began to appear as shown in Fig. 2(a), and after 24 h, some grains had grown to about 700 mm radius as shown in Fig. 2(d). In Fig. 3, those large grains that could be clearly identified as the abnormal grains are marked by arrows. The fine matrix grains grew slowly as can be seen in Figs. 2 and 3.When the heat-treatment temperature was increased to 800°C, distinct AGG behavior was again observed during 24 h, but the number density of the abnormal grains was larger than that observed at ...

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Section: Resultssupporting

confidence: 89%

Temperature Dependence of Grain Boundary Structure and Grain Growth in Bulk Silicon-Iron.

Choi

Yoon

2003

ISIJ International

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“…For this situation Bramwell and Holdsworth calculated that T KT should be approximately 85 % of T N [12]. For the b-parameter experimental values reach from 0.9 (NMR, [13]) to 4.1 (ESR, [10]) which is in agreement with theoretical estimations [11,14].…”

Section: Methodssupporting

confidence: 82%

“…assuming that the contribution of out-of plane correlations of the vortices is very small and thus can be neglected [11]. T KT is the critical temperature of the KT transition.…”

Section: Methodsmentioning

confidence: 99%

Field Dependence of XY-Behavior in Frustrated S = 1/2 Square Lattices

Förster

Garcia

Ponomaryov³

et al. 2014

Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2013)

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The spin dynamics of the layered square-lattice vanadates Pb 2 VO(PO 4 ) 2 and SrZnVO(PO 4 ) 2 is investigated by electron spin resonance (ESR) at various magnetic fields up to 5.7 T and at temperatures above magnetic ordering. The linewidth divergence towards low temperatures is best described by spin fluctuations based on a planar XY type of exchange. Therefore, for both of these frustrated square lattice systems XY-inherent spin topological fluctuations seem to be relevant for the ESR-probed spin dynamics.

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“…4 We built blocks of subsequent configurations, called bins, and averaged the quantities first in the bin. The obtained bin averages themselves can be considered as the results of single measurements.…”

mentioning

confidence: 99%

The hexatic phase of the two-dimensional hard disk system

Jaster¹

2004

Physics Letters A

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We report Monte Carlo results for the two-dimensional hard disk system in the transition region. Simulations were performed in the N V T ensemble with up to 1024 2 disks. The scaling behaviour of the positional and bond-orientational order parameter as well as the positional correlation length prove the existence of a hexatic phase as predicted by the Kosterlitz-Thouless-Halperin-Nelson-Young theory.The analysis of the pressure shows that this phase is outside a possible first-order transition.Key words: Hard disk model, Two-dimensional melting, KTHNY theory PACS: 64.70.Dv, 64.60.CnThe nature of the two-dimensional melting transition has been an unsolved problem for many years [1,2]. The Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory [3,4,5,6] predicts two continuous transitions. The first transition occurs when the solid (quasi-long-range positional order, long-range orientational order) undergoes a dislocation unbinding transition to the hexatic phase (short-range positional order, quasi-long-range orientational order). The second transition is the disclination unbinding transition which transforms this hexatic phase into an isotropic phase (short-range positional and orientational order). An alternative scenario has been proposed by Chui [7,8]. He presented a theory via spontaneous generation of grain boundaries, i.e. collective excitations of dislocations. He found that grain boundaries may be generated before the dislocations unbind if the core energy of dislocations is sufficiently small, and predicted a first-order transition. This is characterized by a coexistence region of the solid and isotropic phase, while no hexatic phase exists. Another proposal was given by Glaser and Clark [2]. They considered a detailed theory where the transition is handled as a condensation of localized, thermally generated geometrical defects and found also a first-order transition. Calculations based on the density-functional approach were done by Ryzhov and

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The critical properties of the two-dimensional xy model

Cited by 2,842 publications

References 11 publications

Temperature Dependence of Grain Boundary Structure and Grain Growth in Bulk Silicon-Iron.

Temperature Dependence of Grain Boundary Structure and Grain Growth in Bulk Silicon-Iron.

Field Dependence of XY-Behavior in Frustrated S = 1/2 Square Lattices

The hexatic phase of the two-dimensional hard disk system

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