Support for the value 5/2 for the spin glass lower critical dimension at zero magnetic field

Andrea Maiorano1,2, Giorgio Parisi1,3

  • 1Dipartimento di Fisica, Sapienza Università di Roma, 00185 Rome, Italy; giorgio.parisi@roma1.infn.it andrea.maiorano@roma1.infn.it.

Related Concept Videos

Support Reactions in Three Dimensions01:27

Support Reactions in Three Dimensions

Support reactions in three dimensions help maintain the stability and equilibrium of various structures and systems. These reactions prevent the system from translating and rotating, ensuring the design can withstand external forces and perform its intended function efficiently and safely. Some of the supports providing support reactions in three dimensions are discussed below:
Ball and Socket Joint is one of the supports allowing free rotation about any axis. This freedom of rotation is...
1.7K
Magnetic Fields01:27

Magnetic Fields

A moving charge or a current creates a magnetic field in the surrounding space, in addition to its electric field. The magnetic field exerts a force on any other moving charge or current that is present in the field. Like an electric field, the magnetic field is also a vector field. At any position, the direction of the magnetic field is defined as the direction in which the north pole of a compass needle points.
A magnetic field is defined by the force that a charged particle experiences...
7.4K
Magnetic Field of a Solenoid01:18

Magnetic Field of a Solenoid

A solenoid is a conducting wire coated with an insulating material, wound tightly in the form of a helical coil. The magnetic field due to a solenoid is the vector sum of the magnetic fields due to its individual turns. Therefore, for an ideal solenoid, the magnetic field within the solenoid is directly proportional to the number of turns per unit length and the current. Conversely, the magnetic field outside the solenoid is zero.
Consider a solenoid with 100 turns wrapped around a cylinder of...
6.0K
Magnetic Field Lines01:19

Magnetic Field Lines

The representation of magnetic fields by magnetic field lines is very useful in visualizing the strength and direction of the magnetic field. Each of the magnetic field lines forms a closed loop. The field lines emerge from the north pole (N), loop around to the south pole (S), and continue through the bar magnet back to the north pole.
Magnetic field lines follow several hard-and-fast rules:
5.8K
Energy In A Magnetic Field01:24

Energy In A Magnetic Field

If a magnetic field is sustained, there must be a current in a closed circuit or loop, implying some energy has been spent in creating the field. If this energy is not dissipated via the circuit's resistance, it is stored in the field.
Take an ideal inductor with zero resistance. Although it's practically impossible, assume that the coil's resistance is so small that it is practically negligible. The loss of the field's energy to dissipate thermal energy (or heat) is thus...
2.8K
Magnetic Field Of A Current Loop01:16

Magnetic Field Of A Current Loop

Consider a circular loop with a radius a, that carries a current I. The magnetic field due to the current at an arbitrary point P along the axis of the loop can be calculated using the Biot-Savart law.
6.4K