Study of the influence of the Metropolis algorithm tuning parameters in the determination of the superconducting critical temperature of Josephson junction networks

Name: Julhiana de Freitas Vargas
Type: MSc dissertation
Publication date: 09/08/2022
Advisor:

Name	Role
Jorge Luis Gonzalez Alfonso	Co-advisor *
Valberto Pedruzzi Nascimento	Advisor *

Examining board:

Name	Role
Dalber Ruben Sanchez Candela	External Examiner *
Jorge Luis Gonzalez Alfonso	Co advisor *
Valberto Pedruzzi Nascimento	Advisor *
Vinícius Cândido Mota	Internal Examiner *

Summary: The statistical method of Monte Carlo via Metropolis algorithm developed in
the MATLAB platform was used to study the behavior of the specific heat of Josephson junction networks as a function of temperature and, consequently, to define their critical transition temperature for the superconducting state. In other words, the algorithm performs a very large sequence of random transitions starting from any initial micro-state of the network until reaching the system energy equilibrium state which is correlated to its critical temperature. Specifically, a systematic study was carried out to verify the influence of the algorithm’s fit parameters (network size, number and size of Monte Carlo steps, number of simulations, among others) in determining the critical temperature. For a 4x4 network, the equilibrium state was not reached with the number of simulations used and a specific heat peak was not found, making it impossible to find the critical temperature. The steady condition was obtained for networks with sizes from 7x7 to 14x14, WHERE the 9x9 and 10x10 networks provided optimized results when the initial input parameters
(PIE) defined in this work were used. The generalized study of the influence of tuning parameters was carried out in a 7x7 network to minimize computational costs, for which a reduced critical temperature value TC = 0.494 ± 0.004 was found when optimized tuning parameters were used . This type of study on the superconducting properties of systems composed of networks of Josephson junctions is essential for a deeper understanding of these devices able to act in several technological applications, such as the manufacture of ultrafast computers and SQUID’S (Superconducting Quantum Interferece Device); the
latter can measure extremely small magnetic fields, such as the fields generated by the electrical currents of the nerve pulses that accompany the activities of the human brain.

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