Lab Report

Objective:

 In this worksheet, you will use the PhET Plinko Probability simulation to explore concepts of phase transitions and symmetry breaking. By varying the rod angle (via binary probability), you will investigate how the distribution of marbles shifts, calculate critical values and analyze the system using power law relationships.

Part 1: Experimental Setup

1. Open the PhET Plinko Probability simulation.

2. Set the total number of marbles (N) to 100.

3. Ensure the "Bounce around pegs" option is selected.

Part 2: Binary Probability (BP) and Rod Angle

The rod angle is determined by binary probability (BP). Use the following BP values to adjust the rod angle:

• BP = 0 → rod angle = 45°

• BP = 0.5 → rod angle = 0°

• BP = 1 → rod angle = -45°

Fill in the table by dropping 100 marbles for each BP value. Perform 10 trials for each BP value and record the number of marbles on the left (N1) and right (N2​) sides.

Part 3: Order Parameter Calculation

1. Order Parameter Formula:

Using your data from the table above, calculate the order parameter M for each BP value and record it below.

Part 4: Critical Binary Probability (BPC)

1. Plot N1​ vs BP and N2​ vs BP on the same graph.

2. Find the intersection point of the two curves. This is the critical binary probability (BPC) where the system undergoes a phase transition.

   • Critical Binary Probability (BPC) = ___________

Part 5: Power Law Fitting and Critical Exponent

The phase transition system conforms to the following power law formula:

Logarithmic Plot: Using your data:

Fit the plot to a straight line to determine the critical exponent β.

• Critical Exponent ( β= ___________ )

Assignment: Virtual PhET Phase Transitions and Symmetry Breaking

1. Research the concept of symmetry breaking in physical systems. Write a short summary (200 words) explaining how it occurs in phase transitions, using examples such as ferromagnetism or liquid-gas transitions.

2. Critical Exponent Research:

   • Find the values of critical exponents for common physical systems (e.g., the Ising model, ferromagnetic materials). Compare them to the exponent you found in your experiment and discuss any differences (150 words).

1. • Problem 1: Symmetry Breaking in Plinko

   • You have an idealized Plinko board where the binary probability is adjusted between 0 and 1. At BP = 0.5, the system is perfectly symmetrical. If at BP = 0.6, the order parameter MMM is measured as 0.4, and at BP = 0.7, M is 0.6, estimate the critical binary probability BPC where the system undergoes a phase transition.

1. • Problem 2: Critical Exponent Calculation

   • In a phase transition experiment, the system follows the power law M∝(BP−BPC)^β. If the critical binary probability BPC is determined to be 0.55 and you measured M=0.2 at BP = 0.6 and M=0.4 at BP = 0.7, determine the critical exponent β.

1. • Problem 3: Phase Transition in a 2D System

   • Consider a 2D Ising model where the system undergoes a phase transition at a critical temperature Tc​. The order parameter (magnetization) near Tc is given by M(T)∝(Tc−T)^β. If the magnetization at T=1.5 K is 0.25 and at T=1.2 K, it is 0.5, with the critical temperature Tc=2 K, calculate the critical exponent β.

1. Worksheet (40%): Completeness and accuracy of theory, calculations, and explanations.

2. Assignment (30%): Detailed report, correct use of formulas, analysis, and discussion of results.

3. Problem Set (30%): Correctness of solutions, step-by-step calculations, and proper explanation.

Each lab group should download the Lab Report Template and fill in the relevant information as you experiment. Each group member should answer the Worksheet, Assignment, and Problem individually. Since each lab group will turn in an electronic copy of the lab report, rename the lab report template file. The naming convention is:

[Short Experiment Number]-[Student ID].PDF

Submit the Lab Report in PDf format