Thermodynamic limit of the first-order phase transition in the Kuramoto model TeX Export

@misc{citeulike:358740, abstract = {In the Kuramoto model, a uniform distribution of the natural frequencies leads to a first-order (i.e., discontinuous) phase transition from incoherence to synchronization, at the critical coupling parameter \$K\_c\$. We obtain the asymptotic dependence of the order parameter above criticality: \$r-r\_c \propto (K-K\_c)^{2/3}\$. For a finite population, we demonstrate that the population size \$N\$ may be included into a self-consistency equation relating \$r\$ and \$K\$ in the synchronized state. We analyze the convergence to the thermodynamic limit of two alternative schemes to set the natural frequencies. Other frequency distributions different from the uniform one are also considered.}, archivePrefix = {arXiv}, author = {Pazo, Diego}, citeulike-article-id = {358740}, citeulike-linkout-0 = {http://arxiv.org/abs/nlin.AO/0509020}, citeulike-linkout-1 = {http://arxiv.org/pdf/nlin.AO/0509020}, day = {19}, eprint = {nlin.AO/0509020}, keywords = {coupled-oscillators, sync}, month = {Oct}, posted-at = {2005-10-21 01:44:35}, priority = {2}, title = {Thermodynamic limit of the first-order phase transition in the Kuramoto model}, url = {http://arxiv.org/abs/nlin.AO/0509020}, year = {2005} }

TY - ELEC ID - citeulike:358740 L3 - citeulike-article-id:358740 N2 - In the Kuramoto model, a uniform distribution of the natural frequencies leads to a first-order (i.e., discontinuous) phase transition from incoherence to synchronization, at the critical coupling parameter $K_c$. We obtain the asymptotic dependence of the order parameter above criticality: $r-r_c \propto (K-K_c)^{2/3}$. For a finite population, we demonstrate that the population size $N$ may be included into a self-consistency equation relating $r$ and $K$ in the synchronized state. We analyze the convergence to the thermodynamic limit of two alternative schemes to set the natural frequencies. Other frequency distributions different from the uniform one are also considered. TI - Thermodynamic limit of the first-order phase transition in the Kuramoto model KW - coupled-oscillators KW - sync AU - Pazo, Diego PY - 2005/Oct/19/ UR - http://arxiv.org/abs/nlin.AO/0509020 ER -