TY - JOUR

T1 - Formation of couples of topological defects in one-dimensional magnetic dipole systems

AU - Dimitrov, R.

AU - Dimitrova, O. V.

AU - Arda, L.

AU - Parmaksiz, Y. E.

AU - Ak, Atilla

N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2022/7

Y1 - 2022/7

N2 - In this study, emphasis is placed on the ordering of three-dimensional point dipoles, with continuous degrees of freedom, arranged on a regular ring at low temperatures and a zero external magnetic field, where interactions are long-range. The perfectly ordered state of the system at low temperatures is destroyed with the appearance of north–north (‘NN’-positive) or south-south (‘SS’-negative) point defects. These defects appear above a certain critical temperature Tc= εf/ ln (N/ 2 - 1) , where εf is the energy of defect formation at low temperatures, and N is the number of dipoles in the model. On increasing the temperature, the number of defects increases and as a result the system undergoes a continuous topological order–disorder transition, similar to the Kosterlits-Thoulless topological phase transitions found in 2-D systems: in one-dimensional systems, instead of vortex defects, we observe coupled, bounded NN-SS point defects. Based on the Boltzmann statistics, an exact law-temperature solution for the model is obtained which may also be extrapolated to high temperatures.

AB - In this study, emphasis is placed on the ordering of three-dimensional point dipoles, with continuous degrees of freedom, arranged on a regular ring at low temperatures and a zero external magnetic field, where interactions are long-range. The perfectly ordered state of the system at low temperatures is destroyed with the appearance of north–north (‘NN’-positive) or south-south (‘SS’-negative) point defects. These defects appear above a certain critical temperature Tc= εf/ ln (N/ 2 - 1) , where εf is the energy of defect formation at low temperatures, and N is the number of dipoles in the model. On increasing the temperature, the number of defects increases and as a result the system undergoes a continuous topological order–disorder transition, similar to the Kosterlits-Thoulless topological phase transitions found in 2-D systems: in one-dimensional systems, instead of vortex defects, we observe coupled, bounded NN-SS point defects. Based on the Boltzmann statistics, an exact law-temperature solution for the model is obtained which may also be extrapolated to high temperatures.

UR - http://www.scopus.com/inward/record.url?scp=85134531750&partnerID=8YFLogxK

U2 - 10.1140/epjp/s13360-022-03052-4

DO - 10.1140/epjp/s13360-022-03052-4

M3 - Article

AN - SCOPUS:85134531750

SN - 2190-5444

VL - 137

JO - European Physical Journal Plus

JF - European Physical Journal Plus

IS - 7

M1 - 837

ER -