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==Edwards Anderson model== | ==Edwards Anderson model== | ||
We consider an Ising model with <math>N </math> spins <math>\sigma_i=\pm 1</math> and i.i.d. coupling <math>J_{ij} </math> drawn from a distribution | We consider an Ising model with <math>N </math> spins <math>\sigma_i=\pm 1</math> and i.i.d. coupling <math>J_{ij} </math> drawn from a distribution <math>\pi(J_{ij})</math>. | ||
It is crucial to assume that the mean value of the couplings is zero, otherwise the model displays ferro/antiferro order. | It is crucial to assume that the mean value of the couplings is zero, otherwise the model displays ferro/antiferro order. | ||
We indicate the avergage over the couplings (namely the average over the disorder) with an overline. In this case we have | We indicate the avergage over the couplings (namely the average over the disorder) with an overline. In this case we have | ||
< | <math><center> | ||
\overline{J_{ij}}=0 | \overline{J_{ij}}=0 | ||
</math></center> | </math></center> | ||
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The | The | ||
For simplicity we assume | For simplicity we assume | ||
< | <math><center> | ||
H= \sum_{ i j } J_{ij} \sigma_i \sigma_j | H= \sum_{ i j } J_{ij} \sigma_i \sigma_j | ||
</math></center> | </math></center> | ||
Revision as of 14:04, 12 November 2023
Spin glass Transition
Experiments
Parlare dei campioni di rame dopati con il magnesio, marino o no: trovare due figure una di suscettivita e una di calore specifico, prova della transizione termodinamica.
Edwards Anderson model
We consider an Ising model with spins and i.i.d. coupling Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle J_{ij} } drawn from a distribution Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \pi(J_{ij})} . It is crucial to assume that the mean value of the couplings is zero, otherwise the model displays ferro/antiferro order. We indicate the avergage over the couplings (namely the average over the disorder) with an overline. In this case we have
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle <center> \overline{J_{ij}}=0 }
Hence the energy associated to a given configuration Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma_i=\pm 1}
with zero average.
The For simplicity we assume
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle <center> H= \sum_{ i j } J_{ij} \sigma_i \sigma_j }