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large systems, it is crucial to have an efficient algorithm to search for such paths. We use the following. First, all intersection points are located. Picking one such point at random, we trace a path starting from this intersection point until it arrives at another intersection point. If the height traveled from the starting to the new intersection point is (formula presented) we stop this search and start again at a different intersection point; if not, we continue tracing the path until then next intersection point is encountered and then repeat the height test. Since most paths connect to field lines which travel in the (formula presented) direction, most such tracings are quickly aborted. However, since each possible transverse loop with (formula presented) contains an intersection point that is at the largest height of all intersection points on that loop, we are guaranteed to ultimately find this path with this search algorithm
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large systems, it is crucial to have an efficient algorithm to search for such paths. We use the following. First, all intersection points are located. Picking one such point at random, we trace a path starting from this intersection point until it arrives at another intersection point. If the height traveled from the starting to the new intersection point is (formula presented) we stop this search and start again at a different intersection point; if not, we continue tracing the path until then next intersection point is encountered and then repeat the height test. Since most paths connect to field lines which travel in the (formula presented) direction, most such tracings are quickly aborted. However, since each possible transverse loop with (formula presented) contains an intersection point that is at the largest height of all intersection points on that loop, we are guaranteed to ultimately find this path with this search algorithm.
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0008669630
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In these works, the authors considered, transverse percolating loops, including those with net winding in the parallel direction, (formula presented) One can show (see Ryu and Stroud in Ref. that the onset of such loops, which in general involve the participation of the field-induced lines and so have (formula presented) coincides with the vanishing of the longitudinal helicity modulus and occurs at the melting (formula presented) rather than the proposed (formula presented) Only by restricting to loops with (formula presented) does one probe (formula presented)
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Phys. Rev. BE A. JaglaC A. Balseiro53, 15 305 (1996). In these works, the authors considered all transverse percolating loops, including those with net winding in the parallel direction, (formula presented) One can show (see Ryu and Stroud in Ref. 5) that the onset of such loops, which in general involve the participation of the field-induced lines and so have (formula presented) coincides with the vanishing of the longitudinal helicity modulus and occurs at the melting (formula presented) rather than the proposed (formula presented) Only by restricting to loops with (formula presented) does one probe (formula presented)
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Jagla, E.A.1
Balseiro, C.A.2
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85038923673
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A. Sudbø (private communication)
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A. Sudbø (private communication).
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