Periodic Reporting for period 4 - LoTGlasSy (Low Temperature Glassy Systems)
Periodo di rendicontazione: 2020-12-01 al 2022-10-31
Since its inception in the mid XIX century, statistical mechanics has aimed to understand the collective phenomena of many interacting elements. The first spectacular success was the derivation of the laws of perfect gases from the collisions of molecules. Until the 1970s, statistical mechanics studied the collective behavior of simple systems.
At that time, statistical mechanics studies discovered that even simple systems could have complex behavior, and this led to the development of the study of complex and disordered systems in physics, which then expanded to applications of all kinds. We are surrounded by complex systems and we ourselves are a complex system.
The importance of this field of research has been recognized in the motivations of the 2021 Nobel in Physics.
In the project Lotglassy we have studied several complex systems with the twofold aim of (i) extending our understanding of the detailed physical behavior of those made of simple elements and (ii) starting the study of those systems made of complex elements.
The project has concentrated mostly on the study of protypical complex systems, namely spin glasses and structural glasses at low temperature, hard spheres at high pressure, and other well-known disordered models, because the advancement in the comprehension of these models is crucial to develop more powerful theories.
However, many real-world applications are nowadays really complex systems whose study requires the same techniques developed in the Lotglassy project. A relevant example are the neural networks at the basis of the modern machine learning and artificial intelligence.
At that time, statistical mechanics studies discovered that even simple systems could have complex behavior, and this led to the development of the study of complex and disordered systems in physics, which then expanded to applications of all kinds. We are surrounded by complex systems and we ourselves are a complex system.
The importance of this field of research has been recognized in the motivations of the 2021 Nobel in Physics.
In the project Lotglassy we have studied several complex systems with the twofold aim of (i) extending our understanding of the detailed physical behavior of those made of simple elements and (ii) starting the study of those systems made of complex elements.
The project has concentrated mostly on the study of protypical complex systems, namely spin glasses and structural glasses at low temperature, hard spheres at high pressure, and other well-known disordered models, because the advancement in the comprehension of these models is crucial to develop more powerful theories.
However, many real-world applications are nowadays really complex systems whose study requires the same techniques developed in the Lotglassy project. A relevant example are the neural networks at the basis of the modern machine learning and artificial intelligence.
The project has been developed studying several different complex models: from spin glasses to structural glasses and hard spheres at high pressure near jamming. We have studied both the thermodynamics of these models, as well as their out of equilibrium dynamics. We also described quantum effects in some of the above complex systems.
A very short list of the main achievements follows:
• We have carried out a very accurate numerical study of the out of equilibrium dynamics of spin glasses at low temperatures. Our predictions have been obtained on time scales long enough to allow for a meaningful comparison with the experimental data.
• Thanks to a new loop expansion around the Bethe mean-field solution developed within this project, we have been able to derive the exact and unexpected value for the upper critical dimension for spin glass models in a magnetic field.
• We have provided a strong numerical evidence that supersimmetry is likely to hold in the random field Ising model in D=5, putting new stronger constraints on the possibile theories for such a model.
• The description of hard spheres at very high pressure has been achieved using mean field equations, which are a great simplification with respect to previous approches. This approach allowed us to obtain analytical estimates for the critical exponents at jamming.
• We have numerically estimated the jamming critical exponents in several models and spatial dimension D, providing a strong evidence for the validity of the mean-field theory down to D=3.
• Quantum effects in hard spheres near jamming have been studied, obtaining precise results on their behavior.
• We have started to put under better theoretical and numerical control the properties of the free energy cost of the interfaces among different glassy states.
• The PI has contributed to the book “Theory of simple glasses" which is a summary of the state of the art in the field.
A very important related event was the Nobel prize in Physics of 2021. In the motivations of the prize many of the subjects of the Lotglassy project were mentioned and this prompted many media reports. In relation to the Nobel prize, we organized the conference “A day with Giorgio Parisi in Rome" which was recorded and streamed by “Rai Cultura”, one of the channels of the Italian public broadcaster.
A very short list of the main achievements follows:
• We have carried out a very accurate numerical study of the out of equilibrium dynamics of spin glasses at low temperatures. Our predictions have been obtained on time scales long enough to allow for a meaningful comparison with the experimental data.
• Thanks to a new loop expansion around the Bethe mean-field solution developed within this project, we have been able to derive the exact and unexpected value for the upper critical dimension for spin glass models in a magnetic field.
• We have provided a strong numerical evidence that supersimmetry is likely to hold in the random field Ising model in D=5, putting new stronger constraints on the possibile theories for such a model.
• The description of hard spheres at very high pressure has been achieved using mean field equations, which are a great simplification with respect to previous approches. This approach allowed us to obtain analytical estimates for the critical exponents at jamming.
• We have numerically estimated the jamming critical exponents in several models and spatial dimension D, providing a strong evidence for the validity of the mean-field theory down to D=3.
• Quantum effects in hard spheres near jamming have been studied, obtaining precise results on their behavior.
• We have started to put under better theoretical and numerical control the properties of the free energy cost of the interfaces among different glassy states.
• The PI has contributed to the book “Theory of simple glasses" which is a summary of the state of the art in the field.
A very important related event was the Nobel prize in Physics of 2021. In the motivations of the prize many of the subjects of the Lotglassy project were mentioned and this prompted many media reports. In relation to the Nobel prize, we organized the conference “A day with Giorgio Parisi in Rome" which was recorded and streamed by “Rai Cultura”, one of the channels of the Italian public broadcaster.
The study of complex systems still requires the development of new and effective techniques, both analytical and numerical, in order to advance the present knowledge. Among the main results of the present project we stress few items representing a clear progress beyond the state of the art and a possibile trampoline for further developments, including applications to socio-economic problems.
• A long standing problem in spin glasses is the exact determination of their upper critical dimension in presence of a magnetic field. This is a crucial infromation at the time of developing any expansion around the mean field solution, needed to better understand the behaviour in D=3 dimensions. In the present project we have clarified that such an upper critical dimension is 8.
It is extremely likely that this result will be used as a starting point for the construction of an 8-epsilon expansion, probably based on the recent M-layer expansion that has been further developed within the present project.
• We have shown in a definitive way the correctness of the mean-field approach to study the jamming state in 3 dimensions (suggesting that the lower critical dimension of hard spheres jamming is 2). This result is likely to boost the use of the mean-field theory in many applications related to jamming (e.g. granular materials).
• In the random field Ising model a supersymmetric theory was proposed but its fate below D=6 was unclear, as different theories existed. On one side we have shown that a new expansion at zero temperature around the Bethe solution can be used and provides new informations. On the other side, we have shown numerical evidence that at D=5 the supersymmetry still describes very well the critical behavior.
These two new results are likely to boost the research on the field of random disordered ferromagnets in the near future.
• By the use of very large scale numerical simulations, we have confirmed that is possible to compare quantitatively spin glass models with experiments on real samples. This crucial step will probably favor further interactions between theoreticians and experimentalists.
PLEASE NOTE THE PROJECT'S PUBLIC WEBSITE IS CURRENTLY UNDER (COMPLETE) RENOVATION.
• A long standing problem in spin glasses is the exact determination of their upper critical dimension in presence of a magnetic field. This is a crucial infromation at the time of developing any expansion around the mean field solution, needed to better understand the behaviour in D=3 dimensions. In the present project we have clarified that such an upper critical dimension is 8.
It is extremely likely that this result will be used as a starting point for the construction of an 8-epsilon expansion, probably based on the recent M-layer expansion that has been further developed within the present project.
• We have shown in a definitive way the correctness of the mean-field approach to study the jamming state in 3 dimensions (suggesting that the lower critical dimension of hard spheres jamming is 2). This result is likely to boost the use of the mean-field theory in many applications related to jamming (e.g. granular materials).
• In the random field Ising model a supersymmetric theory was proposed but its fate below D=6 was unclear, as different theories existed. On one side we have shown that a new expansion at zero temperature around the Bethe solution can be used and provides new informations. On the other side, we have shown numerical evidence that at D=5 the supersymmetry still describes very well the critical behavior.
These two new results are likely to boost the research on the field of random disordered ferromagnets in the near future.
• By the use of very large scale numerical simulations, we have confirmed that is possible to compare quantitatively spin glass models with experiments on real samples. This crucial step will probably favor further interactions between theoreticians and experimentalists.
PLEASE NOTE THE PROJECT'S PUBLIC WEBSITE IS CURRENTLY UNDER (COMPLETE) RENOVATION.