Abstract
We study sampletosample fluctuations in a critical twodimensional Ising model with quenched random ferromagnetic couplings. Using replica calculations in the renormalization group framework we derive explicit expressions for the probability distribution function of the critical internal energy and for the specific heat fluctuations. It is shown that the disorder distribution of internal energies is Gaussian, and the typical sampletosample fluctuations as well as the average value scale with the system size $L$ like $\sim L \ln\ln(L)$. In contrast, the specific heat is shown to be selfaveraging with a distribution function that tends to a $\delta$peak in the thermodynamic limit $L \to \infty$. While previously a lack of selfaveraging was found for the free energy, we here obtain results for quantities that are directly measurable in simulations, and implications for measurements in the actual lattice system are discussed.
Original language  English 

Article number  032118 
Number of pages  12 
Journal  Physical review. E 
Volume  95 
DOIs  
Publication status  Published  8 Mar 2017 
Keywords
 condmat.statmech
 condmat.disnn
Fingerprint
Dive into the research topics of 'Selfaveraging in the random 2D Ising ferromagnet'. Together they form a unique fingerprint.Profiles

Martin Weigel
Person