Phase transition in a stochastic prime-number generator.
We introduce a stochastic algorithm that acts as a prime-number generator. The dynamics of this algorithm gives rise to a continuous phase transition, which separates a phase where the algorithm is able to reduce a whole set of integers into primes and a phase where the system reaches a frozen state with low prime density. We present both numerical simulations and an analytical approach in terms of an annealed approximation, by means of which the data are collapsed. A critical slowing-down phenomenon is also outlined.
Departamento de Matemática Aplicada y Estadística, ETSI Aeronáuticos, Universidad Politécnica de Madrid, Madrid 28040, Spain.
Bartolo
B
Luque
Lucas
L
Lacasa
Octavio
O
Miramontes